M 2007 41 & , .: 210 3608065, Fax: 210 3608197www.volonaki.gr,mail: info@volonaki.gr: : : : , , .ISBN978-960-381-363-7M 7 , 9 , , . , . , : - ( , -, - ) - ( ) - . , . . 11 11.1 ( - )............................................................ 151.2 - .................................................... 411.3 - ........................ 481.4 - ........................ 491.5 ................................................................. 541.6 ................................... 631.7 ........................................................................ 691.8... ... ................... 761.9 ........................................................... 781.10 ............................................................. 81 ...................................... 87 22.1 x + = 0 ........................................................................ 1332.2 x2 + = 0 ....................................................................... 1392.3 ...................................... 1482.4 ..................................................................... 1502.5 - ......................................... 153 .................................... 164 33.1 .................................................... 1953.2 ..... 2003.3 ..................................... 205 .................................... 220 212 44.1 = x2 0 ......................................................... 2394.2 = x2 + x + 0 ........................................... 244 .................................... 252 55.1 ............................................................................................... 2655.2 - ...................................................... 2705.3 ................................................................. 274 .................................... 2831.1 ............................................................................. 2931.2 ........................................................ 3021.3 .......................................................................... 3101.4 ........................................................................................ 3151.5 ......................................................................................... 3191.6 ................................................... 324 .................................... 3292.1 00 1800 ....................... 3512.2 .................... 3572.3 .................. 3612.4 - ............................. 364 .................................... 370 ......................................... 3831 1151.1 ( - ) A. :T = {0,1,2,3,} T = {,-2,-1,0,+1,+2,...} T Q, , ( ) , , , 0. T , . T R, . K . . . , . , , .. , - (+). , (-). 116 : + = + = + ( + ) = (+)+ ( ) = ( ) + 0 = 1 = + (-) = 0 1 = 1, 0 ( ) ( + ) = + . - - . , . = + (-) ( : , 0) , : = 1 = 1. : 0 = 0 . = 0, = 0 = 0. , . , . ( + ) = + 1171. .2. 0 .3. .4. .5. .6. = 0. 7. = 1 = -1.8. .9. .10. 0 0.11. .12. 0 * .. * = {1, 2, 3,..}.13. .14. 2 2. 15. . A 1 .) = ( -4)- (-53)+ (72-4)(53-101)-(-42)( -516)) =53231323+++

)=-(352+1)-[-(3+101)+( -103-107)] ) = (3 -41):(23-41)-)613 ( )6134()4521( : )8143( + . ) A=(-4)-(-53)+(72-4)-(53-101)-(-42)(-516) =-4+53+72-4-53+101-(+ 2032) = = -4 +53+72-4-53+101-1016 =-4 - 4+ 53+53+72+101-1016 =-8+56+72-1015 = =-70560+7084+7020-70105 = -70645 . 118))) = 53231323+++ = 5351031323+++= 51331323++ = 513131323++=13151323++ = 131513133239++ =1328311 =54143. =-(352+1) -[-(3+101)+( -103-107)] =-(55517+ )-[-(1011030+ )+( -1010)] = -522-(10101031 =-522-1021 =-1044-1021 =-1063. = (3-41) :(23-41) - )613 ( )6134()4521( : )8143( + = 41412( ) : ( )4146 -)61618( )6168()4542( : )8186( + = = 411: 45-)619(6747:85 = 54411 -361337485 =511361335620= 511+133 5636 20 =511+133 149 20= =133 79 10511+= 511+93190 = 931 5931 11+931 55 90 = 4655450 10241 + =465510691 .2 A + 5 , .= 3( + 4) (4 - ) + 3( + 1) + 4. = -( - 2) + 3( + ) + 10+ ( - 3) + 2006. + 5 : + ( + 5) = 0,o + = -5 : = 1. + := 3( + 4) - (4 - ) + 3( + 1) + 4 = 3 + 12 - 4 + + 3 + 3 + 4 ==3 + 3 + 15 + = 3( + + 5) + = 3 0 + 1 = 1. =-( - 2) + 3( + ) + 10 + ( - 3) + 2006 = = - + 2 + 3 + 3 +10 + - 3 + 2006 = 2 + 2 + 10 + + 2006 = = 2( + + 5) + + 2006 = 2 0 + 1 + 2006 = 2007. 119 3 , 40 m , 28m .= 3( + 2) 2( + 10) - 3 + 20( + 100) = (4 - 1) + 2( + -15) + + 2003 , 40m2 = 40 28 :2 + 2 = 28, + = 14. + = 3( + 2) - 2( + 10) - 3 + 20( + 100) = 3 + 6 - 2 - 20 -3 + 20 + 20003 + 3 - 2 + 2000 = 3( + ) 2 + 2000 = 3 14 - 2 40 + 2000 == 42 - 80 + 2000 = 1962. = (4 - 1) + 2( + -15) + + 2003 = 4 - + 2 + 2 - 30 + + 2003 == 4 + 2( + ) 30 + 2003 = 4 40 + 28 - 30 + 2003 = 160 + 28 - 30 + 2003 = 2161. 4 : = 3-|-2+5|+3|-4-2| -7, = + 3(4 - 2) 4 ) ) . . = 3-|-2+5|+3|-4-2|-7 = 3-|+3|+3|-6|-7 = 3 - 3 + 3 6 - 7 = 18 - 7 = 11. = + 3(4 - 2)-4 = + 12 - 6 - 4 = 8 - 5.) : + = 0 11 + (8 - 5) = 0 11 + 8 - 5 = 0 - 5 = -19 = 519.) : A B = 1 11 (8 - 5) = 1 88 - 55 = 1 -55 = 1 - 88 = + 5587. 120 5 + = 3 + = + 4, .= 5 - ( - ) (- + ) + 2004, = - (-3 - ) + 2( + ) + 2 + = 5- ( - ) (- + ) + 2004 = 5 - + + - + 2004 = - ( + ) + + + 5 + 2004 = -3 + 4 + 5 + 2004 = 2009.= -(-3 - )+2( + )+2 + = 3++2 + 2 + 2 + = 2+2 + 2 + 2 + 3 =2( + ) + 2( + ) + 3 = 2 3 + 2 4 + 3 = 6 + 8 + 3 = 17.6 N x =23+ . :x + 2 = 1x + 2= -1 x + 2 = 3 x + 2 = -3 x = -1 , x = -3 , x = 1 x = -5 .7 ) N :) = (60 + 57 + 54 ++ 3)-(59 + 56 + 53 ++ 2) , . = (60 + 57 + 54 ++ 3) - (59 + 56 + 53 + + 2) = (60 - 59) + (57 - 56) + (54 - 53) ++ (3 - 2) = 1 + 1 + 1 ++ 1 = 20 1 = 20.: : 1 + 2 + 3 + 4 ++ A=65 ... 15 10 5130 ... 30 20 10+ + + ++ + + +A=65 ... 15 10 5130 ... 30 20 10+ + + ++ + + + = 65 ... 15 10 530 ... 30 20 10+ + + ++ + + + =) 13 ... 3 2 1 ( 513 ..... 3 2 1 ( 10+ + + ++ + + +=510 = 2= 65 ... 15 10 530 ... 30 20 10+ + + ++ + + + =) 13 ... 3 2 1 ( 513 ..... 3 2 1 ( 10+ + + ++ + + +=510 = 2 121 : 1+2+3+4++= 2) 1 ( + (1) .x.N : ) 1 + 2 + 3 ++ 40) 1 + 2 + 3 ++ 100) 2 + 4 + 6 + 8 ++ 200) = 40 (1) :1+2+3++40 =2) 1 40 ( 40 + =241 40 = 20 21 = 420. ) = 100 (1) : 1 + 2 + 3 +...+ 100 == 2) 1 100 ( 100 + = 2101 100 = 50101 = 5050. ) (1) :2 + 4 + 6 ++ 200 = 2(1 + 2 + 3 ++ 100) = 2 5050 = 10100. . () ()1. .2. 0 .3. .4. .5. .6. 0,35 .7. .8. .9. .10.A , ( 0, 0).11. . 22 12212. .13. .14. , > 0 > 0.15. < 0, , .16.A , > 0.17.O -x .18.O .19. 1 -1 .20. 0 . :1. , , :) , ) ) ) .2. = (x - 1821) (x - 2004) (x - 2001) x x = 0 : )0, ) 2006 ) -2004 3. , =1 1

+ - - + 1 )0, ) 1, ) + )- - ) 1.4. x :) 1, ) -8 ) 2 ) 0 )5 5. 0 :) , ) , ) 0 ) 1.33 33 =31=31 21 21 =23+ =23+ 1236. , :i) - ii) 2 + 3 iii) iv) : ;) (i) (ii) ) (i) (iii) ) ( i) (ii) (iii) ) (i) (iii) (iv) ) (ii) (iii) 7.A , :. 0 . . - . 1 . . 1 : , ,, .2 ;2,2 + 1,2 + 3,4 + 1,4 + 3, ( + 1) .3 :) 3 + 4 6 - 36 : (-4) + 2 ) -10: (-4 -6) - [-(4 -2) + (1 -3)] ) (-14) (-4) (3 - 3) (1935 - 678) ) 25:|2-7| + [2 - 4(2 : 4) -3] x 65 = 0x 65 = 0 65 65 6565-423 8 -0,3 516 3,4 32031 -423 8 -0,3 516 3,4 32031 +3, -2, 53, 2,23 , ,3 , 9 , 32+3, -2, 53, 2,23 , ,3 , 9 , 3265-x 1244 + = 4, = -12, := 3 + 3, = + , = ( - 2) - ( - 2) - 2.5A , , = 3, = 16 , :) ) ) , .6 + + = 2001 + 2 = 6 :A = + 2 + 3, = + 3 + 5.7 ) :) := (200 + 196 + 192 ++ 8 + 4) - (198 + 196 + 194 ++ 6 + 4 + 2) ( , - 1999) 8 :9 , + = 4 :10N : , x = - 2( + 4) + 2 = 4( +1) + 7 + 2 .11 x = 850,35 = -150,65 :3x - 3x ( - 1) - [x - ( + 7)] -3 =54 =54-= - 5128-= - 5128, 125, 125 = 250 ... 15 10 5100 ... 6 4 2+ + + ++ + + + = 250 ... 15 10 5100 ... 6 4 2+ + + ++ + + +A=) + 1 2 3 ( )] 2 ( [ ) 2 () 2007 3 3 ( )] 2 ( ) 3 2 ( [ + + + + + A=) + 1 2 3 ( )] 2 ( [ ) 2 () 2007 3 3 ( )] 2 ( ) 3 2 ( [ + + + + + A= ) 5 2 ( 2 ) 1 3 ( 4 ) 2 ( 2)] 2 ( 5 [ 3 5 ) 2 ( 2 ) ( 3 100 + + A= ) 5 2 ( 2 ) 1 3 ( 4 ) 2 ( 2)] 2 ( 5 [ 3 5 ) 2 ( 2 ) ( 3 100 + + 12512 .13 , , , : - 2 = 5,2 - = 7, - 2 = 5 + 3 = 2, + + + . B. 2, .: = :1 = 0 = 1 0 0. , : = +32 33 = 32+3= 35 : = -23 : 2-2 = 23-(-2) = 25( ) = (3)3 = 333 = 273() = (2-3)-3 = 29 = 512= 1 23+ k= 1 23+ k - = 1- = 1() = () = ()- = ()()- = ()( 43)-2 = (34)2( 43)-2 = (34)2 }(52)2 = 2252=254 1261. .2. .i) .ii) A .3. 0 .4. (-) - .5. :i) .ii) .iii) . , .6. i) 1 =1 .ii) (-1) = 1 iv) (-1) = -1 .7. 00 .8. = = .9. i) 2 .ii) 3 .10. = , 0, 1, -1 x = . 127 1 :) (-0,25)17 811) (-4 )60 (-1,25)40) 12100 1,550 6-150) 1o ( ) (-0,25)17 811 = -0,2517 811 = - 0,256 0,2511 811 = - 0,256 (0,25 8)11 = -0,256 211 = -0,256 26 25 = -( 0,25 2)6 25 = -0,56 25 = -0,5 0,55 25 = = -0,5 (0,5 2)5 = -0,5 15= -0,5 1 = -0,5.2o ( )(-0,25)17811 = - (10025)17811 = - (41)17 (23 )11 = -(221)17 233 =-3421233 = -233-34 = -2-1 = -21= - 0,5. ) (-4)60 (-1,25)40 = 460 1,2540 = 420 440 1,2540 = 420 (4 1,25)40 = 420 540 =420 520 520= (4 5 5)20 = 10020 = (102)20 = 1040 2 ) 12100 1,550 6-150 = 15050 10065 , 1 12 = 50 10050 1006 65 , 1 12=(612)100 (65 , 1)50 = 2100 (41)50=2100 (221)50 = 2100 10021=10010022 = 1. ) 12100 1,550 6-150 = 15050 10065 , 1 12 = 50 10050 1006 65 , 1 12=(612)100 (65 , 1)50 = 2100 (41)50=2100 (221)50 = 2100 10021=10010022 = 1. = [(x23)-2(x3)4]: (x3:-1)-3 x= 2007 =20071 A=[(x23)-2(x3)4] : (x3:-1)-3 = (x-4-6x412) : (x-9: 3) = (x-4+4-6+12) :39x= x06 93x = 93 6x = 9x9 = (x) = 200712007 =1 . = [(x23)-2(x3)4]: (x3:-1)-3 x= 2007 =20071 A=[(x23)-2(x3)4] : (x3:-1)-3 = (x-4-6x412) : (x-9: 3) = (x-4+4-6+12) :39x= x06 93x = 93 6x = 9x9 = (x) = 200712007 =1 . 1283 = (-1) + 1 = (-1)2+ (-1)+1 + (-1)= (-1)+ 1 = (-1) + 1. .1 : : = 1 + 1 = 2 2 : = -1 + 1 = 0 = (-1)2+ (-1)+1 + (-1) = 1 + (-1)+1 + (-1) . .1 : , + 1 := 1 + (-1) + 1 = 1.2 : , +1 : = 1 + 1 + (-1) = 1 4 :A = 2101599+ 1099-299 5100B = 279 649 - 325 627= 2101 599+ 1099- 299 5100 = 22 299 599+ 1099- 299 599 5 = = 4 (2 5)99+ 1099- (2 5)99 5 = 41099+ 1099- 51099 = = 1099(4 + 1 -5) = 1099 0 = 0= 279 649 - 325 627 = (33)9 (26)9 (25)5 (23)27 = = 327 254- 225 227 327 = 327 254- 252 327 = 327 252(22- 1) = 328 252 129H O. () ()1. ( - 3)0 = 1. 2. > 0 (-) = .3. 333 = (33)3.4. (-1)+ 1 = - 1.5. + = +.6. (-) < 0 .7. x = 0. 8.A z0 : 3 : = 2.9. (5+3)3 = 53+33.10. (43)5 = (45)3.11. -24 = -(-2)4.12. > 0 - < 0. 13. 5+ 5 = 210.14. 8: 4 = 2.15. (-4)5 (-4)7 = 412.16. - = 1.17. - .18. 2 = 2+1-2 .19. = = .4x = (21)x4x = (21)x 130. :1. (-3)-2 :. 9, .9, . -91 , .91 2. (2x)2 = 641 x :. 3, .3, . 4, .-6, . 63. 810:. 85, . 410, .229, .45, . 0,5 8104. (-6) . :. , . , . 0,. .5.H [(-3)0]5:. 1, . -1, . 35, . -156. 3 = (-3) :. , . , . 0, . .7. () 0 :. 2, . 3, . 28. (-1) :. -1, . , . 1, . 9. (x-3)0 = 1, x :. x = 0, . x = 3, . x 3, . .10. 33 + 33 + 33 + 33 + 33 :. 315, . 533, . 153, . 1515 131 1 :8-3, -7-2, (-3)-5, -44, (-20)5, (4)02 :) 4 5 , ) (-)3 4, ) (-)4: 2, ) 3 8 : -2 3) 24 5)41( 32) 2 ( 8 ) 5 , 0 ( )53 2 5363 2 81 4

3 : = 377+ 377+ 377 = 2102- 2101- 2100, = 299- 449, =217 318- 218 3174 :) 8x = 32,) 3x 42x+ 1 = 192, ) 8 53x-2 = 200, ) 23x = 54 )(32)-2(23) = 481,)3+2 = 15 :) = 58 = (53)2, ) = 28 = 82, ) = 1235 = 742) = 215 = 324, ) = 535 = 719 + 48 719.6 ) :( x -5)(x2)2 = - 31 ) x : = (x + 2)2007+ (x + 3)2008+ (x + 4)20097A x= |- 4-(-3)| = | 3-4| :=1 2 131 2 33 3) 2 ( 2 + XX : 1 213 32 2 ++XX 8A :A = 2) 1 ( 3 4) 1 ( 2+ -2007) 1 ( 11 + + +12) 1 ( 2 3) 1 ( 4 1+ + 9 = (32)4+ 311 : 27 + 33 : 3-5 -2 39 3. 13210 :A = 22000 : [(2550: 599- 351: 925)1999] + (2111)18- 2 21997( 2000)11 ) 2+3 + 2 2 10) = 46+2 -10 46+ 12 612 : = (-1)2007 +[-5-(-22-3)]5 {-[-2-(-12006+1)]}4 = [(-1)10+(-1)11] (24- 32) + 512 : 510-2013A :A = (-1)2007+ (-1)+2+ (1)2+114 = 3 3 43 4 3 5 311 2+ +++ +

.15 : = 2 22 211++ , = 11 77 35 71 2 + 133. x x. .x. , 32 = 9 x = 0 o: , . x : : x0 I ) 0 0 :) 0 > 0 :) . , .) . , . 134 , :1. 0.2. , 0 0.3. 4. 0 .5. .6. . 1 ) , , : ) 0, :))2 :) 135 , .3 . 1364 :A= 36 3 1 14 + + + ,B= 1 8 1 3 7 + += 36 3 1 14 + + +=6 3 1 14 + + +=9 1 14 + +=3 1 14 + + = =4 14 +=2 14 += 16= 4. =1 8 1 3 7 + +=4 16 9 7 3 3 7 9 3 7 8 1 3 7 = = + = ? + = + = + + . 5 x : A=3 x , =x 2 4 , =x 3 2 + 1 + x . A=3 x , : x-3 0 x3. : 4 -2x0 -2x-4 2x 0 . 0 0. . 1. .4 49 25 324 169 196 + + 139 1 :A=2 50+ 4 7 +- 4 3 ,B=25 , 0 + 5 , 2 6 , 3 = 15301122 +210420 2 x, :=1 + x , = x 3 4 , =x 3 9 + 2 x , =x 23 3 + 5 + 54 :A= 5 16-25 20 + 64 2 = 263248,=24 3 2 5 :A= 2) 5 3 ( + 2) 5 1 ( ,B=24 +612-42) 3 6 ( 6A =5 22,=5 22+

:A B - .7N :i) 21,3 23, 82, 54,83,31 2 ii) 2 21,2 34 ,3 22

8N :i) 2 2 3 =2-1 ii)5 2 6 +=1+ 5 1409 : i) 3+x =12-x ,ii)3 x =27 iii) 3x = 12iv) 2x+22 = x+ 210 12. , .11 , , :i)2 2 + -2 ii) 2 2 +2 2 + +2 2 12 :4+ 5 115 4 .13A = 5+2 2 cm = 5-2 2 cm :) .) .14 24 cm2. , . .15 ( =), 18 cm. A 8m, :) .) . 141 1.2 - - ... 8 3 + 4 5, 2 43- 3 5. , - , . , ..x. 3 + x3,52 + 5 . , . , ..x5x ,3, 5 x4, 526 -, . 3 x4. 3 x4 , . 142T 3x4 :4o x1o 5 x, ,.x. 43x2, -6x2, x2 . , , , , .x. 2x54 -2x54, . . , 0 , . , . 1 (3-2) x32 (-2) x32) , ) .) : 3 - 2 = - 2 3- = -2+2 2= 0 = 0 ) :(3 - 2) + ( - 2) = 0 3+ = 2+2 4 = 4 = 1 2 ( - 3)x3 .1 :A - 3 = 0 = 3 .2 : - 3 0 3 3 . 143 . () ()1. .2. 2007 x43 7. 3. ( - 4) x5 5 .4. x42 + x42 .5. 3x-23 .6. 4x-23,6x-23 .7. 4+32 .8. .. .1. (3 + 1)x3+2, -5x32 :. 2 , . 0, . 2, . 4.2. 2x2+ 3x3 :. = 2,. = 3 . = 2 = 3. = 2 = 3.3. 2x . , :. , . , . , . .4. [2x2 (x )2]3 x :. 6 . . 4 . 7 . 12 .5. =3x23. x = -3 -27. :. 1, .1, .27,. 27. 144 1 ; ) -34x23 ) 4-3x23 ) 3x2-3) (4- 5 ) x35 ) 84 4 x ) 23 5 x)48 4 x ) 43x4 2 N : - x x, x4 22 432xx (- 5 x3)2 3 x. N , . x = 5.4 :) A= 3 +23+ 6 5) = (-2) x32 + ( + 3) x23 .5 :) 3x42+ (x2)2) (x2)2x ) (x23)2 (x)3(- 2 3 )x 4 1456 x. A , :) .) .) . ) .) . . , - 1. .2. . 1 :) 2x2 - 4x2,,) 236-6( 2)3, ) 2x3-3x+6x3+3x, , ) 41x5-21x5 ) 3x24+(2x2)2 ) 8 x24- 2 (x2)2 ) 2x2-4x2 = ( 2-4) x2 = -2x2,) 236-6 (2)3 = 236- 636 = = ( 2-6)36 = -436,) 2x3- 3x+6x3 +3 x = (2+6 )x3 = 8 x3 )41x5-21x5 = (41-21) x5 = (4241 )x5= -41x5 146 )3x24+(2x2)2 = 3x24+4x24 = (3+4)x24 = 7x24) 8x24- 2 (x2)2 =8 x24- 2 x24 =( 8 - 2 )x2444 =(2 2 - 2 )x2 = 2 x22 :) 3x4 2x5(-4x)2, ) -3x32 (-2x3), ) 6x2(-2x62) (5x34)) (2x)3 3x2) 3x4 2x5 (-4x)2 = 3x42x516x2 = (3216)(x4x5x2) = 96x11) -3x32 (-2x3) = (-3)(-2)(x32x3) = 6 x43) 6x2 (-2x62) (5x34) = 6(-2)5(x2x6x326) = -60 x108) (2x)3 3x2 = 8x3 3x2 = 24x53 :) 4 x3 : 2x,) -2 x74: (- x 3), )x28: (x56)) 4x3: 2x = 4x3x 21= 2x2 , ) -2x74:(-21x3) =-2x7432 x = = -2(-2) 34 7xx = 4x63 ) 43x28:(52x56) = 438 2 x526 5 x == 20614 7 x = 103 x714 . x () ()1. .2. .3. .4. .5. . 1476. .7. . 1 : )-8x3-4x3+10x3 , ,) 4x2-52x2+21x2 ) 6 2 x2-2 2 x2- 32 x2 ) 103x2-53x2+2x2,,) 56x2-1,6x2+3,4x2 ) 3,45x + 2,45x 2 : ) -4x6x3,) 2x3(-2x2) ,) -3x2(-23) ,) -2x3(-4x)(-5x2)) (-53x2)(625x2) ,) (31x)(6x3)(-21x2) 3 :) 35: (22) 2,) 454:( 4323),) -x2: x4) 24x32 :( -2x)3 ) x3 : (x2)3 ) -273(x)2 : (-3x)2 148 1.3 - . , , .. . 4x3 -7x + 8x4 ., :, .. 42+ 3, .. 4x2 - 2x + 5 B , , . , . , . 4x5 - 2x3+ 2x73:7o x,3 ,10 x , . : (x) Q(x) A(x) ...E: (x) = x3+2x2-x+1,(x) = -54x2-2x+ 2 . A , ..x. (x) = -4x3- 2x + 2. 149A (x) x = () , x . , . , , . . 1.4 . : ( + ) = + : , :( + )( + ) = ( + ) + ( + ) = + + + : , . 150 (x) 0, . () = 0. 1 (x) = 3x3+ 2x2- x + 6x3- 2x + 8) ) x .) = 0 x = -2.) (x) = 3x3+ 2x2-x + 6x3- 2x + 8 = (3 + 6)x3+ 2x2+ (-1-2)x + 8 =(3 + 6)x3+ 2x2- 3x + 8 ) :(x) = (3 + 6)x3+ 2x2-3x + 8. E - :1 : 3+6 0 3 -6 -2 3 .2 : 3+6 = 0 3= -6 =-2 2 2 (x) = 2x3- 3x-1 ) Q(x) = (2x) + 2(-x) + (2)) 2(x) - Q(x). )Q(x) = (2x) + 2(-x) +(2) = 2(2x)3- 3(2x)-1 + 2[2(-x)3-3(-x) -1] + 2 23-32-1 = 2 8x3- 6x -1+ 2(-2x3+ 3x-1) + 16 - 6 - 1 = 16x3-6x -1 -4x3+ 6x- 2 + 9 = 12x3+6 ) 2(x) Q(x) = 2(2x3- 3x -1) - (12x3+ 6) = 4x3- 6x -2- 12x3-6 = -8x3-6x - 8 1513 (x) = 2x3+ x2+ x + 6 Q(x) = (-1)x3+ x2+ ) .) (0)-1= Q(0)+7. ) , , , .) (x) 3 , Q(x) . : i) A -1 = 0 2 . ii) A -1 0 1 3 .) (0) = 2 03+ 02+ 0 + 6 = 6 Q(0) = ( -1) 03+ 02+ = . :(0)-1 = Q(0) + 7 6 -1 = = 5 ) : 2 = - 1 = 1 = 0 = 6 = 3 = 1 = 0 = 6. . () ()1. (x) = 2x2(x4-1) (-x) = (x).2.To (x) = -2 .3. (x) = 0 .4. o (x) (2x) .5. (x) 3 P2(x) 6 .6. (x) = 0x3- 2x + 5 3 .7. (x) = (3x2- x)8(x2- 1) + x10-3 18.8. .9. (x) 3 Q(x) 2 (x) Q(x) 6 . 15210. (x) 3 Q(x) 4 (x) - Q(x) 4 .11. (x) 2 Q(x) 3 2(x) - 4Q(x) 2 .. 1. (x) : (x3+2)(x) +3 = x5- 2x + 1 (x):. , . , . . , . .2. x2 = x + 3, x3 =. x+6. . x2+2x+3, . 4x+3, . 4x2+3 . x2+7E.M.E. 19933.A x=61 (2- )313 ( )21x x : . -12 , )-1 ,)225, ) 1, )12 .. 1992 : A = x6-2x+ x,B= -x3-2x+x2-1 , = x-2+4x+7, = 0,= 53,) . ) . ) . :) (3x2-2x)(4x3+4x),) (x4-2x+2)(x5-2x), ) (x-3)(x-2)x ) (2-3+1)(-2)+(3-2)(2-) (x) = 4x2-2x+3) (-2)=-1-. ) = -4 (0)+4x-2(1)= 3x 123 153 (x) = 2x3-x+1 Q(x)= x-3 ) -(x)2Q(x))2(x) [2Q(x) x+2]) [2(x)-1][Q(x)-2]A(x) = 2x(-x2+3x)(x-2), Q(x) = (x4+1) + x3+x2+x+1, , , , (x) Q(x) . (x) =2x2. ) . ) Q(x) =((x))-1. 5x2-2x +1 4x2-3x+5. A(x) = x2-x+3 ) (x)+A(-x) = 8x+3 ) (1)=10 , (x) =9x3-3x+8x-27 Q(x) = (x3+x)-3x2+(x-3) (x2+3x+9). x , (x) = 500x+50000 . x (x) = 2000-2x . ) x . ) ) 100 .

. 45679108 154 1.5 A . : ) ( + )2 = 2+ 2 + 2:( + )2 = ( + ) ( + ) = 2+ + + 2 = 2+ 2 + 2 (+)2 = 2+ 2 + 2 (+ )2 . ) ( - )2= 2- 2 + 2:( - )2 = ( - ) ( - ) = 2- - + 2 = 2- 2 + 2) - i) ( + )3 = 3+ 32 + 32+ 3ii) ( - )3 = 3- 32 + 32- 3:i)( + )3 = ( + ) (+)2 = ( + ) (2+ 2 + 2) = 3 + 22 + 2+ 2+ 22 + 3 = 3+ 32 + 33.ii)( - )3 = ( - ) ( - )2 = (-)(2-2+2) = 3- 22 + 2- 2+ 22- 3 = 3- 32 + 32- 3) ( + ) ( - ) = 2- 2:( + ) ( - ) = 2- + - 2 = 2- 2) - i) 3- 3 = ( - ) ( 2+ + 2) ii) 3+ 3 = ( + ) (2- + 2) 155:i)(-) (2+ + 2) = 3+2 + 2- 2- 2- 3 = 3- 3ii) ( + )(2-+ 2) = 3-2 + 2+ 2- 2+ 3 = 3+ 31. .2. ( + )2 = 2+ 2, , 0. 3. 2+ 2= 0 = 0 = 0. 1 ) (x + 3)2) ( 3 - 2)2) (2+ 3)2) (4x - )2 ( + )2= 2+ 2 + 2 (-)2= 2-2 + 2)(x + 3)2 = x2+ 23x + 32 = x2+ 6x + 9.)(3 -2)2 = (3)2- 232 + 22 = 92- 12 + 4)(2+ 3)2 = (2)2+ 23+(3)2 = 4 + 62+ 92 = 4 + 152) (4x- )2 = (4x)2- 2 4x+( )2 = 16x2- 8x + 3 2 A ( - ) (2+ 2) (4+ 4) ( + ) = 8- 8. =20071 = 2007 : (-) (2+ 2) (4+ 4) ( + ) = 8- 8 , = 2007 =20071

1563 . :) ( + + )2 = 2+ 2+ 2 +2 + 2 + 2) ( - - )2 = 2+ 2+ 2-2 - 2 + 2. :(2 + + 3)2,(3 -3 - 4)2. )( + + ) 2 = ( + + )( + + ) = 2+ + + + 2+ + + + 2 = 2+ 2+2+ 2 +2 +2 )(--)2 = (--)(--) = 2- - - + 2+ - + + 2 = = 2+ 2+ 2-2 -2 + 2.. : (2 + + 3)2= (2)2+ 2+ (3)2+ 22 + 22 3 + 2 3 =42+ 2+ 92+ 4 + 12 + 6. (3 - 3 - 4)2= (3)2+ (-3)2+ (-4)2+ 23 (-3) + 23(-4)+2 (-3)(-4)= 92 + 92+ 162- 18 - 24 + 244 . ) 2+ 2 = ( + )2- 2 3 + 3 = ( + )3- 3( + )) + = 6 = 5 = 2 + 2 , = 3+ 3, = 4+ 4) :( + )2- 2 = 2+ 2 + 2-2 = 2+ 2( + )3 -3( + ) = 3+32 +32+ 3-32 - 32 = 3+ 3) ) : = 2+ 2 = (+)2- 2 = 62- 2 5 = 36 -10 = 26. = 3+ 3 = ( + )3- 3( + ) = 63 -3 5 6 = 216 - 90 = 226.= 4+ 4 = (2)2+ (2)2 = (2+2)2-222 = 262 -2()2 = 676 -252=676 50 = 626. 1575 ) (3 - )2-3(4 + 5)(4 - 5) ) (3x - )(3x + ) - (x - )(x2+ x + 2))(3 - )2-3(4 + 5)(4 - 5) = (3)2- 23 +2-[(4)2-52] = 92- 6 + 2- 162+ 25 = 72- 6 + 2+ 25)(3x - )(3x + )-(x - )(x2+ x + 2) = (3x)2-2 (x3- 3) = 9x2- 2-x3+ 36 :) ( + )2- ( - )2 = 4) (2007+20071)2 (2007-20071)2 =4 ) (3 + 2)2- (2 + 3)2 = 5 ( - 1)( + 1).)( + )2- ( - )2 = 2+ 2 + 2 (2- 2 + 2) = 2+ 2 + 2+ 2 - 2 = 4) ) = 2007 =20071 (2007+20071)2-(2007-20071)2 = 4200720071 = 4. )(3 + 2)2- (2 + 3)2 = [3 + 2-(2 + 3)][3 + 2 + (2 + 3)] = (3 + 2- 2-3) (3 + 2 + 2 + 3) (-1) (5+5) = 5( - 1)( + 1)7 x, :)x2+ 2+ 6x + 9 = - 25, )2x2+ 2+ 2x + 4x + 4 = 0 )x2+ 2+ 6x + 9 = -25 x2+ 2+ 6x + 9 - + 25 = 0 x2+ 6x + 2+ 8 + 25 = 0 x2+ 6x + 9 + 2+ 8 + 16 = 0 (x + 3)2+ ( + 4)2 = 0 x+3 = 0 + 4 = 0 x = -3 = -4. )2x2+ 2+ 2x + 4x + 4 = 0 x2+ x2+ 2 + 2x + 4x + 4 = 0 x2+ 4x + 4 + x2+ 2x + 2=0 (x + 2)2+ (x + )2 = 0 x + 2 = 0 x + = 0 x = -2 - 2 = 0 x = -2 = 2. 158H O. () ()1. : (x3+ 2)2 = x6+ 4. 2. : ( - )2= (-)2.3. ( + )2= 2+ 2.4. : 2+ 2 = ( + )2- 2.5.6. ( - )2= 2- 2.7. 2+ 2 = 0 = 0 = 0.8. A 2+ 2=2 = .9. (3-)2 = (3-1)2.10. A 2+ 2 ( + )2 = 0 =0 =0.11. -(+ )( - ) = 2-2.12. 3+ 3 = ( + )(2+ + 2).13. (-)3 = -(-)3.14. (x-)2 = x2- 2x(-) +(-)2. B. :1. A - = 6 = 2 + 2- 2 + 3 :. 0 . 39, . 36 . 33 . 81 2. x + = 20 x2- 2 = 80 = - x :. 4 , . -4 . 1 . 10 . .. 1593. ( - 3)2 :. 2+ 9, . 2- 6 + 9, . ( + 3)( - 3) . 2 9 4. A , :. 9, . 11,. 7, . -9, . -11 5. A 2+ + 2 = 10 3- 3= 20 - :. 2,. -2, . 4 . -4 . .6. ( + )2= 2+ 2+ 2, , :. , . , . , . , . .7. x + 4 ,x > 4 x2-16 , :. x + 5, . x-4, . x + 4, . x2-16 , . .8. 2- + 2 :. = ,. = 2, . = 2. . .9. x + = 4 x = 3 x3+ 3 :. 28, . 36, . 64, . 16, . .10. ( + - )2 :. 2+ 2-2+2 - 2 - 2, . 2+ 2+ 2+2 + 2 + 2. 2+ 2+2-2 - 2 + 2, . 2+ 2+ 2+ 2 - 2 + 211. 2 - 2- 2 :.( - )2. ( - )2. ( + )2. ( - )( + ) 160 1 :) ( 2x+3x2)2 , ) (x x 4322 )2, ) ( -3x3+2x)2,) ( 4x2+2x2)2 ) (-3x-2x3)2) ( +1)2 2 :) ( +2)3 , ) (22+33)3, ,) (3-22)3 ) ( 432-4)3 ) (2x-x2)3 ) ( 2 3 )3 3 :) (4x - ) (4x + ), ) (3x2- )(3x2+ ), ) (x- + 2z)(x + -2z) ) (4x - x3)(4x + x3) ) (x - )(-x -)(x2+ 2).4 N :) (2x)3 - 8, ) 27x3- 643, ) 8x3+ 64 ) 64 - (2x)3) (3 + 2)3- (3)35 :) (2x + 3)2 (3x - 1)(3x + 1), ) ( 3 - 2)2- (3 + 2)2+ 3( -1 ) + 3) (1 - x)(1 + x) + (x -1)2+ 2(x -1)) (x - 2)2- (1- 2x)2+ (3x -1)(3x + 1)6 (x) = 3x2- 5x + 1. N :) (x - 10), ) (3 - 2x), ) (-x +1) -2x 7N x.(x) = (x3 - 1)2+ (x3 + 1)2-2(x3-1)(x3+1).Q(x) = (x2 + 1)3+ 3(x2+1)2(1-x2) +3(x2+1)(1-x2)2 + ( 1-x2)3.8A + = 3 = -4 :) 2+ 2, ) 3+ 3 1619 + = 5 = 4 :) 2+ 2, ) 3+ 3, ) 4+ 410 + + = 3 2+ 2+ 2 = 27 :) + + , ) 3 + 3 + 3 - 2007 11 + = 6 2+ 2= 26 :) , ) 3+ 312 x+x1=2 :) x2+21x,)x3+31x) x4+41x 13A xx1=2- , x > 0, :) x2+21x,)(x+x1)2 ,)x+x1 14 :) ( -1) ( + 1)(2 + 1)(4 + 1)(8+ 1) = 16 -1 ) ( + + )2+ ( - )2+ ( - )2+ ( - )2 = 32+ 32+ 32)(2) + -( )2 = 4 15 x, :)x2+ 2x + 1 + 2+ 4 + 4 = 0,)x2+ 2+ 6x + 8 + 25 = 0, )4x2+ 2+ 4x + 2 = -2 16 ) : 2- (-2) ( + 2) ) : 20072- 2005 2009 = 4 17N : (x -2)(x2+ 2x + 4)(x + 2)(x2- 4x + 4) = x6- 64 16218 N : =20072+ 20072 2008+20082 + 2007 .19 :) 27 3+ 272x + 92x + x3) ( + )2+ 2( + )( - ) + ( - )220 , =3 -1, = 3 +1, :) , ) 2 + 2, ) 2- 221 :) (x+)2 = + 2x + , ) (x - 2)2 = +- ,) (+)2 =4x2++ 92 , ) (-)2 =x2+- 222 :) -= (2x - 2)(2+ 2x), ) (x4 - 1) = (-)(+)(+),) -=(x - ) (x2++), ) x3+= (..+ 2)(-2x +)23 :) ( x +)3 = +++ 8, ) ( -2)3= 3-+-24N 39 + 1 28.25 , :) (x - )2= x 2x + + 1, ) (x - )(x + ) = x + 3 - 4 -26 = 900. + = 2 0 = 4 .27 . 1631.6 - , , . , . , . :) , . i) 8x2 - 20x2+ 12x22ii) ( - ) + 3( - ) iii) 4(3x - 1) + x(2 - 6x) i) 8x2 - 20x2+ 12x22 = 4x(8x - 5 + 3x)ii) ( - ) + 3( - ) = ( - )-3( - ) = ( - )( - 3)iii) 4(3x - 1) + x(2 - 6x) = 4(3x - 1) - 2x(3x - 1) = (3x - 1)(4 - 2x) = 2(3x - 1)(2 - x) ) () , : . , . i) 4x3- 8x2+ 3x - 6 ii) x - 5x - 5 + 25 iii) 2x2+ 6x + 42 164i) 4x3- 8x2+ 3x - 6 = 4x2(x - 2) + 3(x - 2) = (x - 2)(4x2+ 3)ii) x - 5x - 5 + 25 = x( - 5) -5( - 5) = ( - 5)(x - 5) iii)2x2+ 6x + 42 = 2x2+ 2x + 4x + 42= 2x(x + ) + 4(x + ) = = (x + )(2x + 4) = 2(x + )(x + 2)) A 2 2 =( + )( - ) , . i) 9x2- 16 ii) (2x - 1)2- 49 iii)x2- 5 i) 9x2- 16 = (3x)2- 42 = (3x - 4)(3x + 4)ii)(2x -1)2 49 = [(2x - 1)-7][(2x - 1) + 7] = (2x - 1 - 7)(2x - 1 + 7) = (2x - 8)(2x + 6) = 2(x - 4)2(x + 3) = 4(x - 4)(x + 3) iii)x2 -5 = x2-( 5 )2 = (x- 5 )(x+ 5 )) 3 3 = ( - )(2+ + 2), 3+ 3= ( + )(2- + 2) , . i) x 3- 8 ii) x3+ 27iii) 27x3- 83i) x3- 8 = x3- 23 = (x-2)(x2+ x + 2)ii) x3+ 27 = x3+ 33 = (x + 3) (x2- 3x + 9)iii)27x3- 83 = (3x)3- (2)3 = (3x - 2)[(3x)2+ 3x2 + (2)2]=(3x - 2)(9x2+ 6x + 42) 165) 2+ 2 + 2 = ( + )2, 2- 2 + 2 = ( - )2 , ( ). i) 2+ 6 + 9 ii) 162- 24 + 92iii) -2+ 2 - 1 i) 2+ 6 + 9 = 2+ 2 3 + 32 = ( + 3)2ii) 162- 24 + 92 = (4)2- 2 4 3 + (3)2 = (4 - 3)2iii)-2+ 2 - 1 = -(2- 2 + 1) = - (-1)2) x2+ ( + )x + . x2+ ( + )x + x2+ ( + )x + = (x + )(x + ) i) x2- 7x + 6 ii) x2+ 3x + 2 iii) -2x2+ 8x - 6 i) x2- 7x + 6, 6 -7. , . : -1 -6. x2- 7x + 6 = (x - 1)(x - 6)ii) x2+ 3x + 2, 3 2. ( ). : 1 2 . 166 x2+ 3x + 2 = (x + 1)(x + 2 ) iii) -2x2+ 8x - 6, -2, x2 1, -2x2+ 8x - 6 = -2(x2- 4x + 3) : x2- 4x + 3. A 3 -4. : -1 -3. x2- 4x + 3 = (x - 1)(x - 3).A -2x2+ 8x - 6 = -2(x2- 4x + 3) = -2(x - 1)(x - 3) 1 :) 4 + 8 ) 62+ 243+ 2 ) 42- 2 + 2 ) 4+ 3)212-23) 2(x - 3) - (x - 3), ) x + - - x ) 9x4- 15x2+ 25 ) 4 + 8 = 4( + 2)) 62 + 243 + 2 = 2( 3 +122 +1) ) 42 - 2 + 2 = 2(22 - +1) ) 4 +3= ( + 1)) 212-23 = 21 (-23)) 2(x - 3) (x - 3) = (x - 3)(2- 1) = (x - 3)( - 1)( + 1) ) x + - - x = (x + ) (x + ) = (x + )( - )) 9x4- 15x2+ 25 = (3x2- 5)22 ) = 3x3 - 3x ) : 3x3=3x) = 3x3- 3x = 3x(x2- 1) = 3x(x - 1)(x + 1) ) 3x3= 3x 3x3-3x = 0 3x(x - 1)(x + 1)=0 3x=0 x-1=0 x + 1 = 0 x = 0 x = 1 x = -1. 167EH O. () ()1. x2- 2 = (x - 2)(x + 2). 2. 2+ 2 = ( - )( + ).3. 2- 2 = -( - )( + ).4. I ( + )- - = ( + )( + 1). 5. ( -) + ( -) = ( - )( - ).6. 1- x2 = (x - 1)(x + 1). . :1. H x3- 5x2+ 6x :. x(x - 2)(x - 3), . x(x + 2)(x + 3), . x (x - 2)(x + 3), x(x + 2)(x - 3) 2. = 4 6 , 2 023 , 5 23 , 1 52 2:. 10, . 100, . 2, . 5. 1 :) 3x2+ 6x ) 4x3- 4x2) 3x2- 3 ) 5x3- 10x2- 5x ) 4x2 - 12x) 3(x - ) ( - x) x + ) 3+ 2 + 2+ 32N :) ( + 1)2- -1 ) x3+ x2+ x + 1 ) (x - 4)( + ) -x + 4 ) x2- 2x + 2) 25x2- 10x + 2) (x + )2- 6(x + ) + 9 3 :) 4 - 2) 16 - 2) x2- 5 ) x 3- x ) 18x2- 82) 4 - 1 ) 9(x + )2- 16(x - )24 :) x2- 3 ) x2- 5 ) x4- x ) x3- 5x2+ 7x - 35 ) x3 - 4x 1685 :) (x2- 4)2- (x + 3)(x + 2)2) (2x - 6)(x2- 9) - (4x - 12)(x - 3)2) 4x2- 4x + 1 - 92) 2+ 2 - x2+ 2x + 2- 2) ( - 2) -4( - 2) - (2 - )2) x3+ 8 - x(x + 2) ) x3- 27 - (x - 3) 6 :) (2 + )(x - 1) (1 - x)( + ), ) ( + )(x + ) - x - ,) (2 -2)(x+)-(x2-2)(-)7 :) x2- 3x + 2 , ) x2- 7x + 6, ) 3x2- 2x - 1, ) -x2+ 7x + 6, ) x2- 4x + 48 :) x2+(3+ 3) x+3 3 )x2+(3+)x+3) x2+(4- 5 )x-4 59 :) x2- 2x - 3 + (x + 1), ) x2+ x + 5x - -6, ) x2+ x - 7x - 4 + 12 10 :) x3- 4x2+ 3x, ) x3- 6x2+ 8x, ) 2x3- 10x2+ 12x, )1 6 2 5 1 02 2 + + x x 11 :) 8x3 -273, ) x3- 83, ) x3+ 1, ) 54x3+ 163) 6 - 1, ) 16x4 + 2x12 ) : = x3 - 5x2+ 6x ) = 0 13 :) x2- 100 = 0, ) 16x3- x = 0, ) x(x + 2)2 = 9x, ) (x - 3)3= (x - 3), ) x2(x - 1)-x + 1 = 0, ) x2(x - 2) - 4x + 8 = 0 14 ) = 2- 4 + 4 + 42) ( 20072 2) 3 22 24 4 4 ++ + 15 :A= 2- 4 + 42 - 16, = 42 - 4 - 4 + 2 = x2 - 4x - 52 = 32 - 4 + 1 - 2 - 2 16916 :A = x4 + 44, = x4 + 4 , =x4 + 9 - 7x2, = x4 + 4 -3x22 = x4+ 4 + x22Z = x2 + 4x - 5217 : = x3- 7x + 6,B = 2x3- 5x + 3, = x3- 4x + 3, = x3+ 2x2- 1 18 :)x+3- x )x+2- x ) x+1- x+2) x+3- x+2-x+219 :) (x + 1)2- 4(x + 1) +4 ) 2+ - 2 - + ( - )2) (x-1)2-6(x-1) + 920 .) 2007 1321 - 2007 321 )9952- 25) 998 1002 + 1 ) 401 399) 20072- 2006 2008 1.7 , () () 0 : , () (), : = + 0 < = 0, = . ., (x) ( ) (x) () (x) 0 (x):(x), - (x) ( ) (x) (), :(x) = (x) (x) + (x) (T ), (x) (x). 170 . (x) = 6x5+ 3x2- 13x4+ 4x3 + 2x-1 (x) = -2x2+ 3x3-x (x) : (x) x :6x5- 13x4+ 4x3- 3x2+ 2x -1 3x3- 2x2-x 6x5 3x3 ( 3536xx = 2x2). T 2x2 .6x5- 13x4 + 4x3 - 3x2 + 2x - 1 3x3 - 2x2 - x2x2 2x2 (3x3- 2x2- x) 2x2( 3x3- 2x2-x) = 6x5- 4x4- 2x3 . , , . 6x5- 13x4+ 4x3- 3x2+ 2x -13x3- 2x2- x-6 x5+ 4x4 + 2x3 2x2-9x4+ 6x3 -3x2+ 2x - 1To 1 =-9x4 + 6x3 - 3x2 + 2x-1 -9x4 1 3x3 ( 3439xx = -3x). -3x .6x5- 13x4+ 4x3- 3x2+ 2x -13x3- 2x2- x-6x5+ 4x4+ 2x32x2- 3x-9x4+ 6x3- 3x2+ 2x - 1 171 -3x, , 3x3- 2x2- x -3x(3x3- 2x2- x) = -9x4+ 6x3+ 3x2 1.6x5- 13x4+ 4x3- 3x2+ 2x - 1 3x3- 2x2- x-6x5+4x4+2x32x2- 3x -9x4+ 6x3- 3x2+ 2x - 1 9x4 - 6x3 -3x2 2x - 1 2 = 2x -1 . ( ) ( ). . :6x5- 13x4+ 4x3- 3x2+ 2x -1= (3x3- 2x2-x)(2x2- 3x) + 2x - 1. () = () () + () :() = () () (x) (x) (x).: , : , , = . 172 1 ) (x4 - 3x3 - 3x2 + 7x + 6) : (x2 - 2x -3) ) x4 - 3x3 - 3x2 + 7x + 6 ) x4 - 3x3 - 3x2 + 7x + 6 ) x4 - 3x3 - 3x2 + 7x + 6 x2 - 2x - 3 -x4 + 2x3 + 3x2x2 - x -2 -x3 +7x + 6x3- 2x2 -3x- 2x2 + 4x + 62x2-4x -60) ) E :(x4 - 3x3 - 3x2 + 7x - 6) = (x2 - 2x - 3)( x2 - x - 2)(1) H (x2 - 2x -3) : : -2 -3 : -3 1. x2 - 2x -3 = (x + 1)(x - 3).O (x2- x -2) : : -1 -2. : -2 1. x2- x - 2 = (x + 1)(x - 2) (1) (x4- 3x3- 3x2+ 7x - 6) = (x + 1)(x - 3)(x + 1)(x - 2) (2).)x4- 3x3 - 3x2 + 7x - 6 = 0. - . (2) .x4- 3x3- 3x2+ 7x - 6 = 0 (x + 1)(x - 3)(x + 1)(x - 2) = 0x - 1 = 0 x - 3 = 0 x + 1 = 0 x - 2 = 0 x = 1 x = 3 x = -1 x = 2. 1732 (x) x2- 2x 4x + 1 (x) = 8x - 5. :(x) = (x2- 2x)(4x + 1) + 8x - 5 = 4x3+ x2- 8x - 2x + 8x - 5 = 4x3+ x2- 2x + 53 (x) = x2+ 2x - 1, [(x) - 2(x + 1) + 3(x - 2) + 24] : (x + 2) (x + 1) = (x + 1)2+ 2(x + 1) -1 = x2+ 2x + 1 + 2x + 2 - 1 = x2+ 4x + 2. (x - 2) = (x - 2)2+ 2(x - 2) -1 = x2- 4x + 4 + 2x - 4 - 1 = x2- 2x - 1. :(x) - 2(x + 1) + 3(x - 2) + 24 = x2+ 2x + 1 -2(x2+ 4x + 2) +3(x2- 2x-1) + 24= x2+ 2x - 1 - 2x2 - 8x - 4 + 3x2- 6x - 3 + 24 = 2x2- 12x + 16 :2x2- 12x + 16x + 2-2x2- 4x2x - 16 -16x + 1616x + 32 48 EH OA. () ()1. 3 2 1 .2. (x) x2-9 : (-3) = (3) = 0. 3. x + 3 (x) (-3) 0. 4. .5. E . 1746. E .. :1. (x) = (x-3)(x3+ 2x - 1) + 7. To (x) x-3 :. 0 . -1 . 3 . 7 . -7 2. (3x3- 2x + 5) : (x - 1 ) :. 6 . 7 . -3 . 5 3. (x3- 5x2+ 4x - 3) : (x - 2) :. 1 . 2 . 3 .4. (x) (x3- 5x + 2) 3. (2) :. 3 . 0 . -3 . 10 5. A (x) :. . . (x). . 1 ) (x3- 5x2 + 7x - 2 ) : (x - 2 ), ) (5x2+ 16x + 3) : (x + 2),) [(x2- 1)(x + 1) -5 ] : (x-3), ) (2x4+ 4x3- 5x + 2) : (x2- 1)) x6: (x - 2)22 (x) = (x3- 4x) (3x2- 3) - 4x + 5. i) ) (x) : (x3- 4x) ) (x) : (3x2- 3)ii)N (x) = 5 - 4x. 1753 ) (x5+ 1) : (x + 1) E 105+1 11. ) (x5- 1) : (x - 1) E 205- 1 19. 4 ) N (2x3- 7x2 + 11x - 4 ): ( x2- 3x + 4).) :2x3- 7x2+ 11x - 4. 5 ) (2x3- 7x2+ 6) : (2x - 1) ) E .) 2x3-7x2+236 (x) (x2- 3x - 2) x2- 2x 3x + 2. (-2).7 (x) 3x3- 2x -1 3x - 1 (1).8 , (x) = x3+ x2+ x + 1 x2+ 1.9 Q(x)= (2+ )x3+ (2+ )x2+ ( + )x-2.A Q(x) x = 1 -4 :) .) Q(x). ) (x) = Q(Q(x)). 176 1.8E.K.. ... - : , . , . : ..., ... ... ... . ... ...) 12x3, 20x423, 16x232) : A = 6x2- 6x, B = 4x2- 8x + 4, = 3x2- 3 ) 12, 20, 16 ... = 240 ... = 4, ... = 240 x433 ... = 4 x2)1) . = 6x2- 6x = 6x(x -1) B = 4x2- 8x + 4 = 4(x2- 2x + 1) = 4 (x - 1)2 = 3x2- 3 = 3(x2- 1) = 3 (x - 1)(x + 1) 2)Y ... ... . : 6, 4, 3 :E.K.. = 12 ... = 1 3) ... . .. . , , ...= 12x(x-1)2(x+1) ... = 1(x-1) 177H O1 , ... . ) x(x + 1), 2x3(x + 1)21. x4(x + 1)3) x4(x - 1), x3(x2- 1) 2.2x3(x + 1)2) x(x + 1)3, x4(x + 1)3.x4(x - 1)(x + 1)4.x4(x - 1) 2 ... .BA 2x 3x(x-2) 9(x-1)218xx2- 43x2(x2- 1)3 , ... . ) 3x(x - 1), 6x2(x - 1)31. x-2) 2x(x2- 1), 4(x - 1)32. 3x(x - 1)) (x2- 4), 3x(x - 2)23. 3x) 15x5,3x(x - 1)34. 2(x - 1)4 ... , .3x(x-1)34x2x59x(x2- 1)6x(x - 1)3x4(x - 1)5 178 1 ... ... :) 2x232,4x32 , 6x23) 6(x)2x, (2x)2x3,8x3) 42,84, 1232 ... ... :) 6(x2- 2), 3(x - ),x3- 3) x4- 4x2+ 9(4 - x2), x3+ 4x2+ 4x - 3(x + 2)2) x2+ x, x2- 1, x3- x3 ... ... :)x2- 3x + 2,x2- 4x + 3, x2- 5x + 6)x2- 4x + 4,x2+ x - 6 ,x2- 4)(x - 1)(x - 1),(x + 1)(x - 1)2,(x + 1)2(x - 1) 4 ... ... :) 2- 2, 2- 4 + 4, 3- 4) 3- 8, 2- 4, 2- 5 + 6 1.9 , . ( ) , , , . . , , . 179 :) 4 43 32xx)13 432+ xx x ) :

4 43 32xx = ) 1 ( 43) 1 ) ( 1 ( 4) 1 ( 3) 1 ( 4) 1 ( 32+=+ =x x xxxx ) . 2 , -4 3. : -3 -1. :3- 3 = ( - )(2+ + 2) : 13 432+ xx x=) 1 ) ( 1 () 3 ) ( 1 (2+ + x x xx x=132+ +x xx 1 :) 23 x ) 11 7+xx) 12 42xx) 11 32+xx) 112xx) x xx2 2 :) 13 x ) 11 2+xx+12 xx)x xx35 3) 422xx x 3 :)232xx) 323xx ) 13 322xx x ) 2 22 22 + ) 1132xx 1804 :) x xx236) 2 2293+xx x ) 2 326 29 6x xx x+ )1 0 22 52+ 5 :) 46 522+ xx x ) 1 6 8422+ x xx x ) x xx x+22 3) 2 222 + a ) 32724 ) ) ) ( ( + ++ + +xx x 6 : = 14 446 53 48 622222+ + + + xx xx xx xx xx x x = (1+3 21 1 1x x x+ + ):3 441x xx = 3 34 2 2 +xx:2 23 2 + x xx 7 : = 2 22 2 32 23 3 ++ +, =2 22 224 4) ( ++ 181 1.10 - , :) = =

. :: = = , , : = . .1. ) (4x2-4) 3 32+ xx )8 422+xx xxx 42 ) (4x2-4) 3 32+ xx = 3 32 ) 4 4 (2+ xx x ==+ + =+ ) 1 ( 32 ) 1 ) ( 1 ( 4) 1 ( 32 ) 1 ( 42xx x xxx x = 32 ) 1 ( 4 x x ) 182)4) 2 () 2 ( 4) 2 ) ( 2 ( ) 2 () 8 4 () 4 ( ) 2 ( 48 422 2 2 2 2= ++ = + =+ xx xx x x xx xx x xxxxx x2. : xx 42:x xx x+ 224 4) 913132)xx 42: x xx x+ 224 4 = 4 4422 2+ x xx xxx = ) 4 4 () ( ) 4 (22 2+ x x xx x x = =2) 2 () 1 ( ) 2 ( ) 2 ( + x xx x x x = 2) 1 ) ( 2 ( +xx x

)) 913132== 3) 9 ) ( 1 (23) 3 () 9 ( ) 1 (2 =) 3 () 3 ) ( 3 ( ) 1 (+ =(-1)(+3) 1 :55+xx2 52 5 1022+ +xx x) x+2) 2 (: 2 222 x + ) +2: + 3 3 ), ,2 :) 81 62 x:3 24 + x ) 224 4 15 10x xx x+ - :2 8252 xx ) 12+xx:(3216 2+++xxxx) ) 4 23:892 32+ ++x xxxx,, , ,)4123xx: 22) 2 (1 2+ xx x 3 :) 2 22 22 2+++) [ ]) 1 (3122 2++xxxx: 22) 1 (2xx )]2141[2+x xx: 8133+xx 183 1 1 := 2007- 2 )31( 2) ( 3 ) ( 3) 3 4 ( 2 10 6 + + + + xz z xx x x + = 2007 2 x x2+ x + 1 = 0 N :)x 0)x3 = 1)x2005+ x2006+ x2007 = 0 3A = x(x - 4) = (x - 6)(x + 2) :) = - 12) + 36 .) x(x - 6)(x - 4)(x + 2) + 36 4 :) (x2- 1)2008+ (2 - 2x)2006+ (x2 - x)2= 0 ) (x3 + 3x2 + 3x)(x3 + 3x2 + 3x + 2) + 1 = 0 5 10 cm 14 cm . .6 x :2006x2+2 -2x-2+2+ 2007(x-1)4+(-1)2= 27 (x) = 2x - 1. ) (0) + (-1) + (1) + (-x) = x ) , :(21) - 2(2) = 3-2 1848 = 2(x+x1) = 2(x-x1), : 2- 2 = 2.9 , 10. . 224cm2, :) .) , .10A - = 1 :( + )(2+ 2)(4 + 4)(8 + 8)= 16 - 1611 x 0 x+x1 = 1 :) x2 - x + 1 = 0) x3 = -1) x2001+ x - 2004 = 0. 12N :) 2 - ( + 1)( - 1) = 1 ) N 6,786952 - 7,78695 5,78695 = 1 13 + = -1 43 = -9 85 :) 2 + 2) (2 - 1)2 + (1 - 2)2 + 28( + )14 = 20072 + 4015 . 18510 1) ;) ;) x + 2 (x) = x3 + 6x2 + 12x + 8 .) ( + )2 = 2 + 2 , 2) 2x2 + 7x + 3. 2x + 1 x.) - = 2 2 + 2 = 20 :i) ii) 3 - 3) :i) x3( - ) + 27( - )ii) (3x - 2 + 3)2 + 6x - 4 + 7) x 3x2 + 5x + 3 = A + B(x - 1) + (x - 1)2 , , . 3 ) 2 23 2+-3 32 3+-6 652 ) A - = (2 3 ) ( 2 3 + ) :A= ( + )2 - 4 + ( - )2007) + 2 +2 = 10 : = 2(+2)2 ( + 2)2 4 ) , , 0 =++ .) i) 200 . . . 6 4 2300 . . . 9 6 3+ + + ++ + + +, ii)x x xx x x x200 . . . 4 2300 . . . 9 6 3+ + ++ + + 18620 1) T ;) .) i) ( x - )2 = - + 4 ii) ( -)2 =+ 25 - 10) (x) = x2 - 3x + 1 ( 1 2 ) 2) 14 + 6 5 3 + 5) : = x4 - x2,B = x3 + 2x2 - x - 2 - ) :i) O 2 + 7 , . ii) : 2 - 2 + 1 , , . 3 . 3 - x 3 + x) (x) . 3 + x) x. ) x 9. ) x ; 187 4 (x) 3. (x) x2 - x 3x + 1. ) (0) P(1)) 2x - 3 (x) (x) 3x2 - x - 1 . 1.1 .. .H O1-3 6 0, 3 -0,8 3,14 2 3 )(-3 2 - 5)x = (-6 -5)x = -11x,) 3(2 - 5x) = -6 + 15x ,) 3(2-5)x = = -3 (-3)x = 9x, ) -3, -2x ) 6 + 3 + 2x + x ) 3x, 2 4i)ii)) ) 1885) ) ) ) 1. ) 2 + 3 4 - 12: (-4)+1 = 2 + 12 + 3 + 1 =18, ) 2 + 3(4 -12):(-4 +1) = 2 + 3 (-8):(-3) = 2 + (-24) : (-3) = 2 + 8 = 10 ) -3 (-2) -5 +4: (-2)-6= 6 -5 -2 -6= -7 ) -8: (-3 + 5) -4 (-2 + 6) = -8(+2) -4 (+4) = -4 16 = -20 2. (5 -4) - (+2) + (-6 +4)-(-7) = -(+1) (+2) + (-2) - (-7) = -1 -2 -2 +7 = 2 4- (-2 +6 -3) + (-9 +6) = 4 +2 -6 +3 -9 +6 = 4 +2 +3 +6 -6 -9 = 0 14 + (-6 + 5 -3)- (-4 -1)(-2) = 14+ (-4) - (-5)(-2)= 14 + (-4) - (+10) = 14 -4 -10 = 0 (-3) (-2) +4 -(+5) - (-1): (-1) = +6 +4- (+5) (+1) = = +6 +4 -5 -1 = 4 2004 ( )3. = 5 m, = 20 m = 25 Km = 45 m + = 20 + 45 = 65 Km.M 25 m4. 1895.6. :7. ) 12 + 5 - 20, ) 8 +9 -1, ) ) 0,35 -6,15 +8,5 8. ) 8-( - ) + ( - 5 -) = 8 - + + -5 - = 8 -5 =3) 2-( + -) - (4 + - )-( -2 -) = 2 - - + - 4 - + + 2 + = 0 ) -2( - 3) + (-7 + 9) -3(+2) = -2 + 6 + (+2) 6 = -2 + 6 + 2 - 6=09. =4-(x - ) - ( - ) = 4 - x + - + = 4 (x + ) + + = 4- (-5) +(-7) = 4 + 5 - 7 = 2 =-(-5- x + ) + (-8 +) - ( - 4) = 5 + x - - 8 + - + 4 = 9 - 8 + x + - ( + ) = 1+ (-5) (-7) = 1 - 5 + 7 = 3.10. : 2( + ) = 56 + = 28 2( + ) = 32 + = 16.= - (9 - 2) - (15 - - 2) = - 9 + 2 - 15 + + 2 = + + 2( + ) 9 -15 = 28 + 32 - 9- 15 = 36 11. -7+ 2+ 5=0-6+-3+ 9=0-5+ 1+ 4=0 190. . 1.) ) ) ) ) ) ) 2.3. 56 14

4.) ) )) ) ) 12.-27 1913.4. 5. = 2. 3 = (3 )2 = 92, .. O1.12 1922. 32 1 3 3 23. 4121 91634 6436 8 6 + +53 5 7 10 14 2

2 2 2 12

12

48

48 43 43 34 34 4. 5. 193 1. 2. 3. 1944. ( ) 5. 6. 7. 1958.9. = + . 50 m2, 8 m2, . . 10.A : 2= 2+ 2 2= 32 + 62 2 = 9 + 36 . : 2= 2+ 2 2= 22 + 12 2= 5 =3.11.) . = AB + B + = 2 = 4 + 4 .) : 196 1.2 - H O1. : ), ), ), )2. : 1): ), ), ) 2) ), ), ), )3) ), ), )3. x x, 5x4 5 x4 1 4 5 -x2 -1 x2 1 2 3 71x25

71 x25 2 5 7 - 3 x4 - 3x4 4 4 4. . 5.O : 1. A , 2. , 3. 4. , 5. , 6, , 7. , 8. .: 1. , 2. , 3. , 4. , 5. .6. , 7. , 8. . . 1.2. :3.4. ) = 3, = 2, ) = 4, = 3, = 2, ) = -4, = 3, = 2 1975.6. x : 2 x + (9-x) 1 7. . = 2. :2= 2+ 2 2=52 + x2. = 25+ x2. x = 12, = 25 + 122 = 169 .. H O1.) ) ) ) 2. 198 1. 2. 3. 4. 5.)x2+ x2+ x2= 3x2 , ) x + x = 2x ) x2+ x ,) . ) . 1996. : 1 = EAE+ = T . . 1.3 H O1. : ) )2. 2 x : ) )3.4.)5.) (x) + B(x) 3 .) 1 2 ( ) 1.2.3. 11004.5.6.(x)-B(x)= 2x3-x2+x-4-(-3x3+5x-2)=2x3-x2+x-4+3x3-5x+2= 5x3-x2-4x-2 (x)+(x)=2x3-x2+x-4+4x2-3x+8=2x3+3x2-2x+4 ) (x)-[A(x)+(x)]= 4x2-3x+8-[2x3-x2+x-4+(-3x3+5x-2)]= = 4x2-3x+8-(2x3-x2+x-4-3x3+5x-2)= 4x2-3x+8-2x3+x2-x+4+3x3-5x+2 = x3+5x2-9x+14 7. ) ( -7x2- 4x + 3) + (x2- 4x + 3) = -6x2- 8x + 7) (-x3+ 5x + 8) - (-2x3+ x2 - 1) = x3- x2+ 5x + 92x2+ 2x - 3 7x2+ 3x - 4 6x2- 2x + 19x2- 3x + 2 3x2+ x - 1 3x2+ 5x -74x2+ 4x - 55x2- x - 16x28. (x)= (-5x2+ 4x - 3) - (x2- 2x + 1) + (3x2+ x) =-5x2+ 4x - 3 -x2+ 2x -1 + 3x2+ x = -3x2+7x - 4 Q(x) = x2+ x + . : = -3, = 7 = -4 11019. O = 2m/sec2 10 sec . : = 2t. : t = 5 : 52 + 20 5 = 125m. 1.4 H O1. 57136 3.) x(2x + 4) = 2x2+ 4x, ) 3x2(x - 2) = 3x3 - 6x2) (x + 5)(2x + 3) = 2x2 + 3x + 10x + 15) (x2 + )(x - 2) = x3 - x22 + + x - 34.i) ) ii) )5.) ) 1.) -3x2(-5x + 2) = 15x3 - 6x22, ) 4x(2x2- x + 2) - 8x = 8x3- 4x2+ 8x - 8x = 8x3- 4x2.) 5x(2x - 3) - 3x(2 - 3x) = -10x2+ 15x - 6x + 9x2= -x2+ 9x, ) 2x(x2 - 32) - 4x(x2 - 23) = 2x3 - 6x3- 4x3 + 8x3=-2x3 + 2x3.2.) (2 - 3)(-4 + 2) = -82 + 4 + 12 - 62 = -82 + 16 - 62) (x2 - 2x + 4)(x + 2) -8 = x3 + 2x2 - 2x2 - 4x + 4x + 8 - 8 = x3,) 3x2(-2x + 3)(5 - x) = (-6x3+ 9x2)(5 - x) = -30x3 + 6x4 + 45x2 - 9x3 = 6x4 - 39x3 + 45x2, ) (4 - 3x)(5 - 2x) -6x(x - 4) = 20 - 8x - 15x + 6x2 -6x2 + 24x= x + 20, ) (2x2 - 3x - 4)(-3x2 + x) = -6x4 + 2x3 + 9x3 - 3x2 + 12x2- 4x = -6x4 + 11x3 + 9x2 - 4x, ) (3x2 - 2x - 52)(4 - x) = 12x2 - 3x3 - 8x2 + 2x2 - 203 + 52x = -3x3 + 14x2 - 3x2 - 2033. ) (3x - 2)(x2 - x)(4x - 3) = (3x3 - 3x2 - 2x2 + 2x)(4x - 3)=(3x3- 5x2+ 2x) (4x - 3)= 12x4 - 9x3 - 20x3 + 15x2 + 8x2 - 6x = 12x4 - 29x3 + 23x2- 6x, )2x(x2 - x + 1)(x - 2) - (x - 1)(2x - 3)(x + 2) = (-2x3 + 2x2 - 2x)(x - 2) -(2x2 - 3x - 2x + 3)(x + 2) = 2. 1102-2x4 + 4x3 + 2x3 - 4x2 - 2x2 + 4x - (2x2 -5x + 3) (x + 2) = -2x4 + 6x3 - 6x2 + 4x - (2x3 + 4x2 - 5x2 - 10x + 3x + 6) = -2x4 + 6x3 - 6x2 + 4x - 2x3 - 4x2 + 5x2 + 10x -3x -6 = -2x4 + 4x3 -5x2 + 11x-6)(-2x + )(x2 - 3x) - (3x - )(4x + )(-2x - 3) = -2x3 + 6x2 + x2-3x2 - (12x2 + 3x - 4x - 2)(-2x -3) = -2x3 + 7x2 - 3x2 - (12x2 -x -2)(-2x - 3) = -2x3 + 7x2 - 3x2 + 24x3 + 36x2 - 2x2 - 3x2- 22x -33 = 22x3 + 41x2 - 8x2 - 334.)(x2 - 4x + 4)(x2 + 4x + 4) - x2(x2 - 8) - 16 = x4 + 4x3 + 4x2 - 4x3 -16x2 - 16x + 4x2 + 16x + 16 - x4 + 8x2 - 16 = 0 )(3 + 8)( - )-( + 2)( - 3) = 3 - 32 + 82 - 8 - + 32 -22 + 6 = 625.) (x) Q(x) = (-2x2 + 5x - 3)(4x - 5) = -8x3 + 10x2 + 20x2 - 25x - 2x + 15 = -8x3 + 30x2 - 37x + 15) (x) [-3Q(x) + 11x - 12] = (-2x2 + 5x - 3) [-3(4x - 4) + 11x - 5] = (-2x2+ 5x - 3) (-12x + 12 + 11x - 5) = (-2x2 + 5x - 3)(-x + 7) = 2x3 - 14x2- 5x2 + 35x + 3x - 21 = 2x3 - 19x2 + 38x - 21 )[(x) -2] [Q(x) + 3] = (-2x2 + 5x - 3 - 2)(4x - 5 + 3) = (-2x2 + 5x -5)(4x - 2) = -8x3 + 4x2 + 20x -10x -20x + 10 = -8x3 + 4x2 -10x +106.E (x) = 3x(-2x + 4)(x - 1) = (-6x2 + 12x)(x - 1)= -6x3 + 6x2 + 12x2-12x= -6x3 + 18x2 - 12x. Q(x) = x3 + x2 + x + : = -6, = 18, = -12, = 0 7. : x 2x + x 2x + ( + 2x)( - 2x) = 2x2 + 2x2 + 2 -2x + 2x - 4x2 = 2. .8. = x(x + 5) = x2 + 5x. T :x + 5 - 3 = x + 2 x -1. 1 = (x + 2) (x-1) = x2 -x + 2x -2 = x2 + x - 2 : x2 + 5x - (x2 + x - 2) = x2 + 5x - x2 -x + 2= 4x + 2 .. 11031.5 H O1.) ) ) ) ) 2. i) ii) iii)) ) 3. ) ) ) ) 4. i) ii)) )5. ) ) ) ) 6. i) ii) iii) iv v) ) ) ) )7. 4 5 1 2 7 8 1. ) (x + 2)2 = x2 + 4x + 4, )( + 5)2= 2 + 10 + 25, ) (2 + 1)2=(2)2+ 2 2 1 + 12 = 42 + 4 + 1, )( + 2)2 = 2 + 2 2 + (2)2= 2 + 4 + 42, ) (3 + 2)2 = (3)2 + 2 3 2 + (2)2= 92 + 12 + 42) (x2 + 1)2 = (x2)2+ 2x2 + 1 = x4 + 2x2 + 1.) 11042.) (x-3)2= x2 -23x + 32 = x2- 6x + 9, ) ( -5)2 = 2 - 2 5 + 52 = 2 -10 + 25) (3 - 1)2 = (3)2 - 2 3 1 + 12 = 92 - 6 + 1, ) (2 - )2 = (2)2 -2 2 + 2 = 42 - 4 + 2,) (3 - 2)2 = (3)2-2 3 2 + (2)2= 92 - 12 + 42,)(x2 - 2)2 = (x2)2 -2 x2 2+ 22 = x4 - 4x2+ 4, ) (2 -)2 = (2)2-22 + 2= 4- 23+ 2,) (2x2- 5x)2 = (2x2)2- 2 2x2 5x + (5x)2= 4x4 -20x3+ 25x2,3.4. ) (x + 3)2 = x2 + 6x + 9 ) (- 4)2 = 2 - 8 + 16) (4x -)2 = 16x2 - 8x + 2) (x2- 2)2= x4 - 4x2 + 425. ) (x +1)3 = x3 + 3x21+ 3x 12 + 13 = x3 + 3x2+ 3x + 1,) ( + 4)3=3+ 32 4 +3 42 + 43= 3 + 122 + 48 + 64, ) (2 +1)3 = (2)3 + 3 (2)2 1 + 3 2 12 +13 = 83 + 3 42 + 6 + 1 = 83 + 122 + 6 + 1, ) (3 + 2)3 =(3 )3 + 3 (3)2 2 + 3 3(2)2+ (2)3= 273 +3 92 2 + 9 42+ 83= 273+ 542+ 362+ 83,) (x2 + 3)3 = (x2)3+ 3 (x2)2 3 + 3 x2 3 + 33= x6 + 9x4 + 9x2 + 27,) (2 + )3 = (2)3 + 3(2)2 + 322 + 3 = 6 + 34 + 34 + 3 = 6 + 35 + 34 + 3) (x -2)3 = x3 -3x2 2 + 3x 22+ 23= x3 - 6x2 + 12x +8 ) ( -5)3 = 3-3 2 5 + 3 52- 53= 3 - 152 + 75 - 125 ) (3 -1)3= (3)3 -3(3)2 + 3 3 12 - 13 = 273 -3 92 + 9 -1 = 273 - 272 + 9 -1 i) (2x -3)3 = (2x)3 - 3(2x)23 + 3 2x(3)2 - (3)3 = 8x3 -3 4x2 3 + 6x 92 - 273 = 8x3 - 36x2 + 54x2 - 273i) (2- 2)3= (2)3- 3(2)2 2 + 32 22 - 23 = 6 - 64 + 122 - 8 i) (2 - 2)3 = (2)3-3(2)2 2 + 32(2)2- (2)3 = 6 - 45 + 3242 - 83=6 - 45 + 124 - 836. ) (x -1)(x +1) = x2 -1,) ( -2)( +2) = 2 - 22= 2- 4, ) (3 -)(3 +) = =32 - 2 = 9 - 2, ) (x + 4)(4 - x) = (4 + x)(4 - x) = 42 - x2 = 16 - x2) (x - )(-x -) = -(x - )(x + ) = -(x2 - 2) ) (2x + 7)(2x - 7) = (2x)2- (7)2 = 4x2 - 492 11057. (x) = (x - 3)2 + (3x + 1)2 - 10(x - 1)(x + 1) = x2 - 2 3x + 32 + (3x)2 + 2 3x 1 + 12 - 10(x2 -12) = x2 - 6x + 9 + 9x2 + 6x + 1 - 10x2 + 10 = 20 8. ) ( - )( + )(2 + 2)(4 + 4) = (2 - 2)(2 + 2)(4 + 4) = (4 -4) (4 + 4) = 8 - 8) 9 11 101 10001= (10 - 1)(10 + 1)(102 + 12)(104+ 14) = 108-18 = 100000000-1 9.10. ) (x - 3)(x2 + 3x + 9) = x3 - 33 = x3 - 27 ) ( + 2)(2 - 2 + 4) = 3 + 23 = 3 + 8 ) (2 + 1)(42 - 2 + 1) = (2)3 + 13 = 83 + 1,) (1 - )(1 + + 2) = 13 - 3 = 1 - 311. ) (x - 4)2 + (2x + 5)2 = x2 - 2 4 x + 42 + (2x)2 + 2 2x 5 + 52 = x2 -8x + 16 + 4x2 + 20x + 25= 5x2 + 12x + 41, ) (x2 -1)2 - (x2 - 3)(x2 + 3) = x4 - 2x2+ 1- (x4 - 9) = x4 - 2x2+ 1 - x4 + 9 = -2x2+ 10) (x + )2 -(x - 2)(x + 2) + (2x - )2= x2 + 2x + 2 - [x2-(2)2] + (2x) 2 - 2 2x +2 = x2+ 2x + 2-x2+ 42 + 4x2 - 4x + 2 = 4x2- 2x + 52.) (3x - 4)2+ (3x + 4)2-2(3x - 4)(3x + 4) = (3x)2-2 3x 4 + 42+ (3x)2+ 2 3x 4 + 42 - 2[(3x)2- 42] = 9x2- 24x + 16 + 9x2+ 24x + 16 -2 (9x2- 16) = 18x2+ 32- 18x2 - 32= 64) (2+1)3+ (2 -1)3 = (2)3+ 3(2)2 1+ 32 12+13+(2)3 -3(2)21+3 2 12- 13= 83 + 122+ 6 + 1 + 83 - 122 + 6 - 1 =163 + 12) (+2)3- (+2)(2-2+4) = 3+322+ 322+23- (3+23)= 3+ 62 + 12 + 8 3 - 8 = 62+12) (2+)3 -(2 - )3 =(2)3+ 3(2)2 + 322 2 + 3 -[(2)3 -3(2)2 +32 2-3]=6 +35 + 34 +3- 6 +35 - 34 +3 = 65 +23) (4 - 1)3-(8 + 1)(8 - 1)=(4)3 - 3 (4)2 1 + 3 4 1 + 13 - [(8)2 - 1] = 643-3 162+ 12 + 1 - (642- 1)= 643- 482+ 12 +1- 643+ =-482+13+1 110612.13.14.15.16.) (x-2)2-(2x-)2+3x2=x2-2x2+(2)2-[(2x)2-22x+2] +3x2= =x2-4x+42-(4x2-4x+2)+3x2=x2-4x+42-4x2+4x-2+3x2=32) (-3)2+(3+2)(3-2)-(3-)2=2-23+(3)2+(3)2-(2)2-[(3)2-23+2]= 2-6+92+92 42-(92-6+2)=2-6+92+92 42-92+6-2=2+42 ) (x-1)(x+1)3-2x(x-1)(x+1)=(x-1)(x3+3x2+3x+1)-2x(x2-1)= =x4+3x3+3x2+x-x3-3x2-3x-1-2x3+2x=x4-1 ) (2+2)2-(2)2=(2)2+222+(2)2-422=4-222+4 ) (-4)2+(2-3)2=2-24+42+ (2)2-223+32=2-8+16+42-12+9= =52-20+25. ) (2x2+2x)2+(2x+1)2=(2x2)2+22x 2x2 +(2x +(2x) )2 2+22x1+1= x4+8x3+4x2 2+4x +4x+1= 4x4+8x3+8x2+4x+1 ) x=(3+ 5 )(3- 5 ) = 32- ( ) 52=9-5=4 ,) x2-2 =(x-)(x+)= =(3+ 5-3+ 5)( 3+ 5+3- 5)=2 5 6=12 5 ) x2+2 = =(x+)2-2x=(3+ 5+3- 5 )2-24=62-8=36-8=28. ) x3+3 =(x+)(x2+2-x)=( 3+ 5+3- 5 )(28-4)=624=144. ) (+5)2-(-5)2=2+25+2)5(-[ 2-25+2)5(]= 2+10+22 5- 2+10-22 5= 20. ) =2005(2005+20055)2-(2005-20055)2 = 20 T 2=2+22=(4x+1)2+(3x+2)2 B2= (4x)2+24x+1+(3x)2+23x2+22 B2=16x2+8x+1+9x2+12x+4 B2 = 25x2+20x+5. A : B2=2+2. 2+2=12+(5x+2)2=1+(5x)2+25x2+22=1+25x2+20x+4=25x2+20x+5=2 , : (+)2=2+2+2,(-)2=2-2+2 :4) ( ) (2 2= + . 2 2) ( ) ( += ) 2 ( 22 2 2 2+ + + = 4=4 4 1107) 2) (2 2 2 +=2) 2 (2 2 2 2 + +=222 2 2 2 + +== =22. ) ) = +2) (2 2 2. =21 =212) (2 2 2 += =2122 102 2=496= 24 cm2 To : +, -, (+)(-)=2-2To 2- .2 . 1.6 .H O1.2.3.4.5.6.7.8.9.17.18. 1108 1.2.3.4.10.11. 1109 ) 2x2-32=2(x2-16)=2(x2-42)=2(x-4)(x+4),) 28-72 =7(4-2)=7(2-)(2+) )2x3-2x=2x(x2-1)=2x(x-1)(x+1), ) 5x2-80 = 5(x2-16)=5(x-4)(x+4) ) 2(x-1)2-8=2[(x-1)2-4]=2[(x-1)-2][(x-1)+2]=2(x-1-2)(x-1+2)=2(x-3)(x+1) 2=2-22 = (-)(+). ) 2=(53-28)(53+28)2=2581=59 =45 , ) 2=(0,37-0,12)(0,37+0,12)2=0,250,49=0,50,7=0,35, ) 2=(26-10)(26+10)2=16362=16362=46=24. ) x2-49=0 x2-72=0 (x-7)(x+7)=0 x-7=0 x+7=0 x=7 x=-7) 9x3-4x=0 x(9x2-4)=0x[(3x)2-2]=0 x(3x-2)(3x+2)=0 x=0 3x-2=0 3x+2=0x=0 x=32 x= -32 . ) x(x+1)2=4x x(x+1)2-4x=0 x[(x+1)2-22]=0 x(x+1-2)(x+1+2)=0 x(x-1)(x+3)=0 x=0 x-1=0 x+3=0 x=0 x=1 x= -3 )(x+2)3=x+2 (x+2)3-(x+2)=0 (x+2)[(x+2)2-1]=0 (x+2)(x+2-1)(x+2+1)=0 (x+2)(x+1)(x+3)=0 x+2=0 x+1=0 x+3=0 x=-2 x=-1 x=-3 5.6.7.8.9.10.11. 1110 ) x3-27= x3-33=(x-3)(x2+3x+32)=(x-3)(x2+3x+9) ) 3+8=3+23=(+2)(2-2+22)=(+2)(2-2+4) ) 3+64=3+43=(+4)( =(+4)(2 2-4+4 -4+16)2) ) 8x3-1=(2x)3-13=(2x-1)[(2x)2+2x1+12]==(2x-1)(4x2+2x+1) ,) 273+1=(3)3+13=(3+1)[(3)2-31+12]= (3+1)(92-3+1). ) 3x3-24=3(x3-23)=3(x-2)(x22+2x+22)=3(x-2)(x2+2x+4) ) 164+2=2(83+1)=2[(2)3+1]=2(2+1)(4 - 2+1) ) 34R3-343=34(R3-3)=34(R-)(R2+R+2) ) 4+4=(3+3)=(+)(2- +2)) (x3-27)=(x-3)(x2+3x+9) ) 8x3+3 =(2x+)(4x2-2x+2) ) 3-83=(-2)(2+2+42)) 3+1253 =(+5)(2-5+252) ) x2-2x+1=(x-1)2, ) 2+4+4=(+2)2, ) 2-6+9=(-3)2, ) 2+10+25=(+5)2, ) 1-4+42 =(1-2)2, ) 9x4+6x2+1=(3x+1)2 ) 42-12+9 = (2-3)2,) 16x2+8x+2 =(4x+)2, ) 252-10+2= = (5-)2,(+)2-2(+)+1=(+-1)2, i)i) 22) 33( 9 29 = + , i) x2+x+41=(x+21)2

) 3x2+24x+48=3(x2+8x+16)=3(x+4)2, ) -2+4-4 =-(2-4+4)=-(-2)2) 22-8+82 = 2(2-4+42)=2(-2)2, ) 43+122+9=(42+12+9)= (2+3)2

) =xx+2x+=x2+2x+2 ) 2=x2+2x+2 2=(x+)2 =x+. = + = 21+21 = 21(+)=21(x+1)(x+x+2)==21(x+1)(2x+2)=212(x+1)(x+1)=(x+1)2. A 2=(x+1)2 = x+1. 12.13.14.15.16.17.18. 1111)x2+3x+2=(x+1)(x+2), ) 2-4+3=(-1)(-3), ) (2+5+6)=(+2)(+3) )2+6+5 =(+5)(+1)) x2-7x+12=(x-3)(x-4) ) 2--12=(+3)(-4) ) 2-9+18=(-6)(-3)) 2+3-10 =(+5)(-2) ) x2+(2+ 3 )x+2 3 =(x+2)(x+ 3 )) x2+(2+3)x+6=(x+2)(x+3) ) x2+(3- 2 )x-3 2 =(x+3)(x- 2 ) ) 22+10+8=2(2+5+4)=2(+1)(+4) )32-12-15 = 3(2-4-5)= 3(+1)(-5) ) x2-7x+6= (x2-7x+6)=(x-1)(x-6) . ) 14531821-1453821=1453(1821-821)=14531000=1453000 )8012+199801 = 801(801+199)=8011000=801000 ) 9982-4=9982-22=(998-2)(998+2)=9961000=996000 ) 9991001+1=(1000-1)(1000+1)+1=10002-12+1=1000000-1+1=1000000 ) 9992+2999+1=(999+1)2=10002=1000000 ) 972+697+9=(97+3)2=1002=10000 ) x22-42-x2+4 =2(x2-4)-(x2-4)=(x2-4)(2-1)=(x-2)(x+2)(-1)(+1). ) x4-1+x3-x= (x2)2-1+x(x2-1)=(x2-1)(x2+1)+x(x2-1)=(x2-1)(x2+x+1)= (x-1)(x+1)(x2+x+1). ) x3(x2-1)+1-x2 =x3(x2-1)-(x2-1)=(x2-1)(x3-1)=(x-1)(x+1)(x-1)(x2+x+1)) (x2+9)2-36x2=(x2+9)2-(6x)2=(x2+9-6x)(x2+9+6x)=(x-3)2(x+3)2 ) 2-2+2-+=(-)2-(-) = (-)(--1) ) x2-2x+2-2=(x-)2-2 =(x--)(x-+)) 1-2+2-2=1-(2-2+2)=12-(-)2=(1-+)(1+-) ) 2-x2-10+25=2-10+25-x2=(-5)2-x2=(-5-x)(-5+x) ) 2(x-1)(x2-4)-5(x-1)(x-2)2=2(x-1)(x-2)(x+2)-5(x-1)(x-2)2= (x-1)(x-2)[2(x+2)-5(x-2)] = (x-1)(x-2)(2x+4-5x+10)=(x-1)(x-2)(-3x+14) i)(2-4)2-(+2)2=(2-4--2)(2-4++2)=(2--6)(2+-2)= (+2)(-3)( -1)(+2) i) (2+2-2)2-422=(2+2-2)2-(2)2=(2+2-2-2)(2+2-2+2)= =[(-)2-2][(+)2-2]=(--)(-+)(+-)(++) i) (x2+9)(2+4)-(x+6)2=x22+4x2+92+36-2x2-12x-36=4x2+92-12x=(2x-3)2 =x-x-2+2=x(-1)-2(-1)=(-1)(x-2). x .19.20.21.22.23.24. 11121.7 .H O1.i) ii) iii)) ) )2. 8 35 7 5 2 9 6 33.) ) ) ) ) 1.)x+22x3+x2-3x+6 -2x3-4x2 -3x2-3x+6 x2+6x 2x2-3x+3 3x+6 -3x-6 0 2x3 + x2 - 3x + 6 = (x + 2)(2x2 -3x + 3))3x+1 6x3 - x2-10x+5 -6x3- 2x2 -3x2-10x+5 3x2+x -9x+5 9x+3 2x2-x-3 8 1113 6x3 - x2 - 10x + 5 = (3x + 1)(2x2 - x -3) + 8)x-16x4 -x2+2x-7 -6x4+6x3 6 x3 x2+2x-7-6 x3+6x2

5x2+2x-7 -5x2+5x 6x3+6x2+5x+7 7x-7 -7x+7 0 6x4 - x2 + 2x - 7 = (x -1)(6x3 + 6x2 + 5x + 7))2x-14x3+5x-8 -4x3+2x2 2x2+5x-8 -2x2+x 6x- 8 -6x +3-52x2+x+3 4x3 + 5x - 8 = (2x - 1)(2x2 + x + 3) -5)x2-x+2x5-x4+3x2+2 -x5+x4-2x3 -2x3+3x2+2 2x3-2x2+4x x2+4x+2 -x2+x-2 5x x3-2x+1 x5 - x4 + 3x2 + 2 = (x2 - x + 2)(x3 - 2x + 1) + 5x 1114)03x2+x-19x4- x2+2x-1-9x4+3x3-3x23x3- 4x2+2x-1-3x3+x2-x-3x2+x-13x2-x+1-3x2-x+1 9x4 - x2 + 2x - 1 = (3x2 - x + 1)(3x2 + x - 1))2x2-38x4-6x2-9-8x4+12x2 6x2-9 -6x2+904x2+3 8x4 - 6x2 - 9 = (2x2 - 3)(4x2 + 3)) 3x2-13x5-2x3-4 -3x5+x3

-x3-4 x3- x31 - 431 x x3-31x 3x5 - 2x3 - 4 = (3x2 - 1)(x3 - 31)-31 x - 4 11152. ) 6x2+22x+12 -6x2-4x 3x+2 18x+12-18x-12 02x+6 3.A (x) :(x) = (x2 - x + 1) (2x + 3) + 3x + 2 = 2x3 + 3x2 - 2x2 - 3x + 2x + 3 + 3x + 2 = 2x3 + x2 + 2x + 54. Q(x): (x) = 0 ) 6x3-7x2+9x-182x-3 -6x3+9x2 2x2+9x-18 -2x2+3x 12x-18 -12x+18 03x2+x+6 )x+1x4+4x3+6x2+4x+1-x4-x3 3x3+6x2+4x+1-3x3-3x2 3x2+4x+1 -3x2-3x x+1 -x-1 0x3+3x2+3x+1 5.) : x22+x+1 2x4-x2+5x-3-2x4-2x3 2+2x -2x3 2+x +5x-32x3 2+2x -2x3x2+3x-3 2x -2x+3 0 -3x2- 3x+3 x+3 2x3+10x2+2x+20 -2x3-6x2 4x2+2x+20 -4x2-12x-10x+20 10x+30 502x2+4x-10 1116) E :x4 - 2x3 - 8x2 + 18x - 9 = (x2 - 9)(x2 - 2x + 1) = (x - 3)(x + 3)(x - 1)26. ) (x4 - 2x3 - 8x2 + 18x - 9) : (x + 1) x+1x4+4x3+6x2+4x+1-x4-x3 3x3+6x2+4x+1-3x3-3x2 3x2+4x+1 -3x2-3x x+1 -x-1 0x3+3x2+3x+1 E o x + 1 )x4 + 4x3 + 6x2 + 4x + 1 = (x + 1)(x3 + 3x2 + 3x + 1) =(x + 1) [(x3 + 1) + 3x (x + 1)] = (x + 1)[(x + 1)(x2 -x + 1)+3x(x + 1)] = (x + 1)(x + 1)(x2 -x + 1+ 2x) = (x + 1)(x + 1)3(x + 1)47. 3 + 3 = ( + )(2 - + 2). 2 - + 2.8. ) : (x) = 4x2 - 6x + 7.) 4x2 - 6x + 7 2 . :4x2 - 6x + 7 = 4x2 -20 + 20 - 6x + 7 = 4(x2 5)-6x + 27. (x) = (x3 + 2)(x2 - 5) + 4(x2 - 5)- 6x+27 = (x2 - 5)(x3 + 2 + 4) -6x+27 = (x2 - 5)(x3 + 6) -6x+27. (x) = -6x+27 11179.x-16x3+-6x3+6x2 6x2+ -6x2+6x 6x2+6x+6 6x+ -6x+6 +6 + 6 = 0 = -6 10. (x - 1)2 = x2 - 2x + 1. (2x3 - x2 - 4x + 3) : (x2 -2x + 1)x2-2x+12x3-x2-4x+3 -2x3+4x2-2x 3x2-6x+3 -3x2+6x-3 2x+3 0 2x + 311. To x2 , x 2. E 5x+4, 45x2+ 56x + 162 : (5x+4) 9x+4 . 45x2 + 56x + 16. 11181.8 E.K.. H O1. 42 12. 4x32x(x - 1) 9(x - 1)26x212x36x2(x - 1) 18x2(x - 1)2x2(x - 1) 4x3(x - 1) 2x2(x - 1) 9x2(x - 1)2 8x58x58x5(x - 1) 72x5(x - 1)23. 24 34. 1119 1.) ... 72x334) ... 30x232) ... 24x23(x - )(x + )2... 6x22... 5 ...x(x + )2. ) ... 12(x + )(x - )3) ( - 1)( - 2), ( - 2 )( + 2), ( - 2)( + 2) ... 2(x-)... (-1)(-2)(+2) , ... (-2)) 2( - 1), ( - 1)( - 1)( + 1), ( - 1)2... 2( - 1)2( + 1), ... ( - 1) 1.9 .H O1. ) ) ) ) )6 3 4 1 52.) ) ) ) ) ) 3.) x - 2, ) + , ) x + 1, ) x, ) 2( + ), ) (x + 2)24. x 0. 1. ) x 4, ) 25, ) -1, ) x 0 x 3. 2. ) 3264=xx, ) 4 1232= , ) x xx4 8222= ,) 23 2105a=22, ) xx++44=1, ) 11=-1, ) 2) 2 (2 = 21 , ) ) ) ( () ) ( ( =1 1120 )23) 2 ( 264 262+=+=+ x x xxx xx, ) 33) 3 ) ( 3 () 3 ( 399 32+=+ = , ) xxx xxx x=++=++) () (22, ) 2) 2 ( 5) 2 () 2 ) ( 2 ( 5) 2 () 4 ( 5) 2 (2 0 52 2222+=+ == , )xxx xx xx xx 4) 4 () 4 ) ( 4 (41 622+=+ =, ) 11) 1 () 1 ) ( 1 (1 212 22+=++ =+ + ) 2 2243 6+xx x= =+ +xxx xx x23) 2 ) ( 2 () 2 ( 3, ) 3 32 2 + +=) ) ( (2 22 2 + + + + ) 21) 2 () 2 ) ( 1 (4 42 32 22++=++ +=+ ++ +xxxx xx xx x, ) 8 64 522+ + = =21) 4 ) ( 2 () 4 ) ( 1 (= , )=+ =+ ) 1 () 1 2 ( 22232 3 = 11) 1 ) ( 1 () 1 (2+=+ . ) 34) 3 ) ( 1 () 4 ) ( 1 (3 2) 1 ( 4 ) 1 (2++=+ + = + + xxx xx xx xx x x, )= + 9 49 ) 3 (22 = 3 23) 3 2 ) ( 3 2 () 3 ) ( 3 () 3 2 ) ( 3 2 () 3 ) ( 3 ( ) 3 (=+ + + =+ + + ) = 13) 1 ) ( 1 ) ( 1 () 1 ) ( 1 ( 32 2+=+ + + , ) 2 32) 1 ( 4 ) 2 ) ( 1 ( ++ += = ) 1 (] 4 ) 2 ) [ ( 1 (22+ + =2) 2 2 ) ( 2 2 ( + = =2) 4 ( aa 4 . =+ + + =+ + + + +=+ +) 1 ) ( 1 ) ( 1 () 3 3 ) ( 1 () 1 ) ( 1 () 2 1 2 ) ( 2 1 2 (1) 2 ( ) 1 2 (2 2 2 42 2 6. : AB = 5 t. H =214t2= 2t2. :tt t22 52+= ttttt+ = +2522252m/sec 3.4.5. 1121 1.10 H O1.) ) ) ) ) ) ) ) 2. ) 2x,) x, ) 4x, ) 21+xx, ) 12+xx, ) ) xxx1 12= , ) 43314 9= xx, ) 12x2x 91=34x, )= 2 234632 ) (-52) 103 = -23, ) (-23)(-24)= 6 ) 8x : x6=8x6x=342x, ) 21: (- )3=3(12 )= - 31, ) (-2323 : ) = -3 2 323131 = , ) (- = )4( : )222 3 x x- = )4(222 3xx = 2x.) x x xx xxxxx 8) 3 (4 ) 3 ( 234 6 22 2=+ +=++, )1) 5 ) ( 2 () 2 ) ( 5 (5225 = ++ =++ , ) ) ( ) ) ( () (3 22 32 22 33 2 +=+ =xxx x xx xxxxx, )=++ + 23642 22 = 1) 2 ( ) 3 ) ( 2 () 3 ) ( 2 ) ( 2 (=+ + + + ,)=++ ++x xx xxx x36 542222=+ + + + +) 3 ( ) 2 ) ( 2 () 3 ) ( 2 ) ( 1 (x x x xx x x x = 21+xx,) ) 3 2 ( ) 3 2 () 3 ( ) 3 2 ) ( 3 2 (3 239 12 49 42 2222+ + + =+++ =3 23++ 1.2.3. 1122)34) 4 ( 341 5541 54:54=++=++=+ +xxxx x x, ) ++12 1:11 2== 12 111) 2 1 (2 1111 2 =++ =++, )2 ( : )2( ++ )= =(- 121)2 =++,) 22) 1 (:1 + + = 2 2) 1 (1++=) 1 (1+ ) 2221) ( ) (:x x xxx xxxx xx xx=++=++ )124 2) 4 2 ) ( 2 () 2 ) ( 2 (4 22:8422 2 32=+ + ++ =+ +xx xx x xx xx xxxx ) 28 8: )24 412(++++xxxxxx = ) 1 ( 22) 1 ( 822) 1 ( 412=++++xxxxxxxx )=++=++++=++++1) 2 ( 2:12]32) 1) 3 ( 2[ :12)3216 2( :12xxxxxxxxxxxxxxxx

21) 2 ( 2112=++xxxx, ) 32)16 2:12(++++xxxxxx=(32)6 2112++++xxxxxx= = 22) 3 ( 2) 2 (32) 3 ( 22++=++++xxxxxx B. 1.) ) ) ) ) ) 2. ) :13++xx3.)6 + xx, )66+ x,) 1 + xx, ) 26+ x, ) x1 ) x8 4.5. 1123 ) ,1 1 xxxxx x+= + = +) x x213+= =+++ ) 1 () 1 ( 2) 1 (3x xxx xx=++ ) 1 () 1 ( 2 3x xx x =) 1 (2) 1 (2 2 3+=+ x xxx xx x, ) 1 12 =2 2 21 1= , ) 12 12 2+ =

) 1 (1) 1 (2 1) 1 (2) 1 (12 222 22 22 222 22 +=+ +=+++,)= 336 22x xx133333 33) 3 ( 22=== xxx xxx xx. )=++=++) 2 (4) 2 (624262 ) 2 () 2 ( 3) 2 (4 6++=+ =3,)=+4 2446 32 ) 2 ( 24) 2 ) ( 2 () 2 ( 3+ + =2223 = = 21 , ) 23 6 1 2 21xxx ++= =+ ++ ) 6 ) ( 6 ( ) 6 ( 21x xxx = ) 6 ( 21) 6 ) ( 6 ( 26) 6 ) ( 6 ( 22) 6 ) ( 6 ( 26x x xxx xxx xx= ++=+ + + ) ==+=+ x x x x x xxx x xx 6 3 9) (3) (9 3 92 2 )=+ + =+ +++ ++=++ ++) 3 ) ( 1 (2 2) 3 ) ( 1 () 3 ( 3) 3 ) ( 1 (7133 472 =32) 3 ) ( 1 () 1 ( 2+=+ ++ . =1 ) 1 ) ( 1 () 1 () 1 () 1 (11222 332 3332=+ + + +=+ +=+ + . )11) 1 ) ( 1 (111111122 =++ =+=+=+xxx xxxxxxxxxx, )=+ 112 =11) 1 ) ( 1 () 1 (11 211 222222+=+ =+ =+ , ) 31111+ += 1.2.3. 1124 )= 1 1) ) ( (2 2 2 2 + === +1 )=+=+) 2 (824 22824 22x x x xxx x x xx =xxx xx xx xxx xx x xx xx x 2) 2 () 2 ) ( 2 () 2 (4) 2 (8 4 4 4) 2 (8 4 ) 2 (2 2 2+=+ == + + = + . ) ) 2 ) ( 2 (1 6 2222341 6 222232 2 + +++=+++ x xxx x xxx x = = = ++= ++ + = ++ + + ) 2 ) ( 2 (6 3) 2 ) ( 2 (1 6 2 4 2 6 3) 2 ) ( 2 (16 2 ) 2 ( 2 ) 2 ( 3 x xxx xx x xx xx x x = 23) 2 ) ( 2 () 2 ( 3= ++x x xx , )=++ 33226 5622

) 3 ) ( 2 () 2 ( 3) 3 ) ( 2 () 3 ( 2) 3 ) ( 2 (62 + = ) 3 ) ( 2 () 2 ( 3 ) 3 ( 2 62 + =23) 3 ) ( 2 () 3 ) ( 2 () 3 ) ( 2 (62+= + = + . ) 2 22 2 22 ++ xxx xx= ) ) ( (22 2 2 + ++ x xxx xx = =+ + +) ) ( (2 ) ( ) (2 2 2 x xx x x x

= ) ) ( (22 3 2 2 3 + + +x xx x x x= =+ + + + ) ) ( () ) ( (2 2 2 2 x xx x x x x ==+ + + + ) ) ( () ( ) ) ( (2 2 x xx x x x x) ) ( () 2 ) ( (2 2 + + + x xx x x= ) () (2++xx = x+) ( )3 411 ) (1 2 1 23+++x xxxx= [3 41 3 4] () 1 2 ) ( 1 2 () 1 2 ( ) 1 2 ) ( 3 (+ ++ +xxx xx x x x)= = 1 223 4) 1 2 ( 2]) 1 2 ) ( 1 2 (3 4[ )3 42 4] () 1 2 ) ( 1 2 (2 3 6 2[2 2+= += + + x xxx xxxxx xx x x x x ) [222 2) 1 (3: ]) 1 (313++xxxxxx=[3) 1 (]) 1 (3) 1 ) ( 1 (3222++ +xxxxx xx = 4.5. 1125) ( ) ( ) ( ) ) ( ([3) 1 (]) 1 ) ( 1 () 1 ) ( 3 () 1 ( ) 1 () 1 ) ( 3 (222 2 ++ ++ +xxx xx xx xx x= =+ + + +3) 1 () 1 ( ) 1 () 1 ) ( 3 ( ) 1 ) ( 3 (222xxx xx x x x = 3113 3 3 3311) 1 ) ( 3 ( ) 1 ) ( 3 (22 22+ + + + =++ + +x xx x x x x xx xx x x x= 12311) 3 ( 222+=+x x xx, ) (1- ) ) (22 2 +++=()()() () () [22 22 2 +++ + == =+ + +) () (2 22 22, )= + + ) ( : ) 1 (2 2 = = + + ) ( : ) (3 3 2 2 =+ + 3 3 2 2: = +=+ + +=+ + 1) ) ( (2 22 23 32 2. = +xxx3 3= + + + = ++ + x x x xxx x x2 22 2) ) ( ( = x2+2x+2 =(x+)2. ) x=56 = 44 : 10000 100 ) 44 56 ( 4 4 5 644 5644 562 23 3= = + = + ) 2+2=(22)12+ xx+222)11(+xx= 1 21 21 242 42 42 22+ ++ ++ + x xx xx xx = =11 21 22 42 4=+ ++ +x xx x. ) x=100 A=100012001 1002002=+, B=1000199991 1001 10022=+. A ) 2+2=1, , 100019999,10001200 1. 6.7. 1126 1 1. 2233 ==, K= (-0 2004 1 2 3] ) 2004 2 [ ( )212 ( 4 )231 ( )23 + + ++ = = -0 1 2) 2006 ( )2124( 4 )2322(827 + + + = - = + + 1 )23( 4 )21(82 71 2 = - 1 )32( 4 ) 2 (8272+ + = - 1384827+ =-2424246424962481+ =-24217 2. ) 2+1 :( - + 3)2 + 1 + ( - - 3)2 + 1 = = ( - + 3)2 + 1 + [-(- + 3)]2 + 1== ( - + 3)2 + 1 + (-1) 2 + 1 ( - + 3)2 + 1== ( - + 3)2 + 1 - ( - + 3)2 + 1 = 0 ) 2 :(x - - )2 -( + - x)2 = (x - - )2 -[-(x - - )]2 = (x - - )2 -(-1)2(x - -)2= (x - - )2-(x- - )2= 0 3.=2 22 26 4 ++ xx x=2222222 226 4++ xx x=1 ) (1 6 ) ( 422++ xx x==+ + 1 )21(1 )21( 6 )21( 422 =4520455444151411 3 1= = =+=++ +, = 3 23 2 33 2 2 ++ xx x =33323332333 2 2++ xx x= = 454411413 1 )81( 21 )21(3 )21( 2 )21( 21 ) (3 ) ( 2 ) ( 22323=+ =++ + =+ + =++ xx x454154541641=+ = = 3 11274. ) (1 - x) = -2(1 - x)2 + 2(1 - x) + 800 = -2(1 - 2x + x2) + 2 - 2x + 800= = -2 + 4x - 2x2 + 2 - 2x + 800 = -2x2+ 2x + 800 = (x).) x = 100 (100) = (-99)(100) = -2 1002+ 2 100 + 800 = -2 10000 + 200 + 800= = -20000 + 1000 = -19000 = (-99)5.) .) ) + + = 0 0, 0. : 3 + 3 + 3 - 3 = 0 3+ 3+ 3= 3.) = x - , = - , = - x, + + = x - + - + -x = 0 O ) (x - )3 + ( - )3 + ( - x)3 = 3(x - )( - )( - x) 6.7. )x4 - 22 = x2(2 - 2) x4 - 22 = x22 - 2x2 x4 - 22 - x22 + 2x2 = 0 x2(x2 + 2) -2(x2 + 2) = 0 (x2- 2)(x2 + 2) = 0 x2-2 = 0 x2+ 2 = 0 () (x - )(x + ) = 0 x - = 0 x + = 0 x = x = -.)x3 + 3 = x2 + x2 x3 + 3 - x2 - x2 = 0 x2(x - ) - 2(x-) = 0 (x - )(x2- 2) = 0 (x - )(x - )(x + ) = 0 x = x = -.8. ) x2 + 4x + 3 = (x + 1)(x + 3),x2 + 2x - 3 = (x - 1)(x + 3)) = =+ ++ ++ += ++++ + ) 3 ) ( 1 (1) 1 ) ( 1 (1) 3 ) ( 1 (13 21113 412 2 2x x x x x x x x x x x = =+ + +++ + +++ + ) 3 ) ( 1 ) ( 1 (1) 3 ) ( 1 ) ( 1 (3) 3 ) ( 1 ) ( 1 (1x x xxx x xxx x xx =) 3 ) ( 1 (3) 3 ) ( 1 ) ( 1 () 1 ( 3) 3 ) ( 1 ) ( 1 (3 3+ =+ + +=+ + +x x x x xxx x xx.9. ) = x(x + 3) = x2 + 3x,B = (x + 1)(x + 2) = x2 + 2x + x + 2 = x2 + 3x + 2 = + 2 1128) ) = + 2, : = 2 + 2 + 1 = 2+ 2 + 1 = ( + 1)2) x(x + 1)(x + 2)(x + 3) +1 = + 1 = ( + 1)2= [x(x + 3) +1]210.) = 16x4 + 8x2 + = (16x4 + 8x2 + 1) = (4x2 + 1)2. = 2. 2 = (4x2+1)2 = 4x2+ 1.) : (4x)2 + (4x2 -1)2== 16x2 + (16x4 - 8x2 + 1) = 16x2 + 16x4 - 8x2 + = 16x4 + 8x2 + . ) = 4x2 + 1 11.) 2 + = ( + 1). , + 1 , ( + 1) .) ( + 1)3 - 3 = 3 + 32 + 3 + 1 -3 = 32 + 3 + 1 = 3(2 + ) + 1 = = 3 ( + 1) +1. (1) ( + 1) 2 ( ). (1) = 3 2 + 1 = 6 + 1. ( + 1)3 - 3 = 6 + 1. 1.) , : = 2 + 1, = 2 + 1, ,.2 - 2 = (2 + 1)2-(2 + 1)2 = 42 + 4 + 1- (42 + 4 + 1) = 42 + 4 + 1 - 42 - 4 -1 = 4(2 + ) -4(2 + ). 2+ , 2 + , 2 + = 2, 2 + = 2, ,. 4(2 + ) -4(2 + ) = 4 2 - 4 2 = 8( - ) = 812.)x-1x6-1 -x6+x5 x5 -1 - x5+x4 x4 - 1 -x4+x3 x5+x4+x3+x2+x+1 x3- 1 -x3+x2 x2-1 -x2+x x-1-x+1

0 1129A x6 - 1 = (x - 1)(x5 + x4 + x3 + x2 + x + 1). O x = 7 :76 - 1= (7 - 1)(75 + 74 + 73 + 72 + 7 + 1) = 6 (75 + 74 + 73 + 72 + 7 +1) == 6x+1x5+ 1 x5-x4 -x4+1 x4+x3 x3+1

-x3-x2 x4-x3+x2-x+1 -x2+1 x2+x x+1 -x-1 0

x5 + 1 = (x + 1)(x4 - x3 + x2 - x + 1) 215 + 1 = (23)5 + 1 = 85 +1 = (8 + 1)(84 - 83 + 82 - 8 + 1) = 9 (84 - 83 + 82 - 8 + 1) = 913.) 1) 1 (1) 1 () 1 () 1 (1) 1 (111=+ = == x x ) 1 ( x xx xx xx xx xxx xxx x ) x=2 21112 11 = x=3 31213 21 = x=4 41314 31 = x=200820081200712008 20071 = 2008200720081200820082008112008 20071. . .4 313 212 11= = =+ +++. : 2 21332.1 x + = 0 : x + = 0 , . x . . x , . . x. M : 0 x = 0 .M . :0 x = 0 x = . (1)1. 0 (1) x=

2. A = 0 0 (1) 0 x = 3. = = 0 (1) 0 x = 0 . 1 :1) 2) 3) 4) ( ). 0, . :) ... . ) . . 2134 1. R: ) 4x - 68 5 + x = 39 2 x, ) 51-101 + x = 102 x ) .. : 12, : 124x-1268 5 + x=1239 2 x3x-2(5x+8)=4(2x-9) 3x-10x-16=8x-363x-10x-8x=16-36 -15x=-20 x=1520x=35 ) ... : 10, : 1051-10101 + x=10102 x 2-(x+1)=2-x2-x-1=2-x -x+x=2-2+1 0x=1 . 2. :) 3(x- -5 2)=4(x-1)) 32 4 x+21 x=6x+3) 3(x-2) =4(x-1) -5 3x-6=4x-4-53x-4x=-4-5+6 -x=-3 x=3 . ) 32 4 x+21 x=6x+3632 4 x+621 x=6(6x+3) 2(4x-2)+3(x-1)=6(6x+3)8x-4+3x-3=36x+18 8x+3x-36x=4+3+18 -25x=25 x=-1 -1 . . A. () ()1. 3x + 2 = 0 .2. 0 x=0 .3. 3x = 0 4. 0x = 0 0.5. 3x = 3 . 21356. -3x + 6 = 0 7x - 14 = 0 .7. x = x . 8. x= x=1 9. x + = 0 , x + = 0 .10. x = -5 0 .11. x = 5 .12. 0x = (2+ 3)0 .13. 3 x - 27= 0 3 . 14. x = 2 x = 2.15. x = 16. x = 0, .17. 0 x = (2 + 1) 18. 4(2x - 1) = 5(x - 1) + 1 -3x . 1. 5x+2 = x+4(x+21)) :. . . . 02. 4 x = 0 :. x= -4 . x= 41. x=4 . . x = 0 . x= - 41

3.H x = 0 :. = 0 . = 1 . 0 . . 21364. ( + 3) x = 3 , :. 3 . -3 .0 . 25. A 2 3x - 2 + = 0 :. -4 . 0 . 4 . -26. 4x -3 = 5 :. 2x -1 = 5 . 3x - 2 = 4. x - 3 = 4 . 2x - 5 = 7 7. x + x - 1 + x - 2 ++ x -19 = 290 :. 14 . 24 . 34 . 44 . 54 8. x = :. 0 0 . = 0 0 . 0 . 0 = 0.9. 2 32 : 8. :. 3x + 2 = x - 4, . 3x + 2 = x - 3, . 4x + 2 = x - 4, . 4x - 4 = x - 2 10. A ( - 1) x = + 5 2x + = x + 2 , :. 1, . -1, . 2, . 0 11. ( - 1) x = ( - 1)( + 1). :. = 1, . = -1, . = 0 . 1. : 4(3x - 2) -4x = 3(x -1) + 5 N x = 2 . x= 32007 .2. Q :) 3-2(x-3) x-1= 3(x-6)+2) 42 3 x-21 x=31 4 x) 32 3 x-41 4 x = x-3 3. R : ) 2x = 5x, ) 2(x - 1) = 2x - 2, ) 0x = 1) 21 3 x+32 4 + x= 3x) 4x-52 3 + x=21 x 21374. N R :) 2(3-|x|) = 4 ) 4(|x|-2) - 4 =4 ) |x| -(3-|x|) = 15. N R :) 31 x= 2-3(x-3)+2x)54 7 + x = x+25 3 x ) 3 2635 368 x x x x+=+ ) 27 5 x-37 2 + x=3x-14 ) 61 23243 = xxx x 6. R :) 41 x-[ ] 3 ) 11 25(32 ++ x x =1 ) 3{x- 2 5 ) ] }53( 2 1 [41 3 =+ xxxx ) 21[8- 0 5 ) ] 5 ( 3236 [ ) ] 52( 22= + + + xx x x 7. 33 x+32-3x= -11 = (-3)2008+52 3 +2-2 8. :A(x) = 32 + x -4x) (x + 3) ) (x + 3) = 0 ) (x) +1 = A(x) -x 9. :(3x - 2)2007+ 5(x3 - 1) = 1 2(x - 1) -3 =- 2- (2x - 1) 10. :435+ x = -23 + x

(1)) (1) ) :2 = 7 + x 3 = 24 + , x (1) 21381. 47 10 5 . .2. 40 . 5 , 2 . 165 . ;3. 317419 , .4. 703. , 4 3. .5. 19% 1428 . ;6. A 31 , 41 , 61 9 . ; 2139 2.2 ( ) 2. 2 . 2 x :x2 + x + = 0 0 , , . . O :x2 + 8 = 0: = 1, = 0, = 8-2x2 -8 -3x = 0: = -2, = -3, = -8 4x + 3x2 = 0: = 3, = 4, = 0 . :A = 0 = 0 = 0 .1) A = 0 : x2+ x = 0, 0. :x2 + x = 0 x(x + ) = 0 x=0 x+=0 x = 0 :N : ) x2 + 3x = 0, ) x2 = 6x. ) x2 + 3x = 0 x(x + 3) = 0 x = 0 x + 3 = 0 x = 0 x = -3 .) x2 = 6x x2- 6x = 0 x(x -6) = 0 x = 0 x - 6 = 0 x = 0 x = 6 2) = 0 : x2 + = 0, 0 1o : ( ) x2 + .:N ) x2 - 4 = 0, ) 4x2 - 20 = 0)x2 - 4 = 0 x2 - 22 = 0 (x - 2)(x + 2) = 0 x -2 = 0 x + 2 = 0 x = 2 x = -2 2140) 2s: T : x2= :A > 0, , . < 0, . = 0 x = 0 ().:N ) 3x2 = 27 ) 5x2 - 20 = 0. :(x + ) ( x + ) = 0 .. : x2 +5x - 6 = 0. -1 + 6 = 5 -1 6 = -6 (x-1) (x+6)= 0 x - 1 = 0 x + 6 = 0 x = 1 x = -6.1) x2 + x + = 0 , : + = = 2) x2+ x + = 0 0 :) 4, x2.) 2+ 2 2 - 2 . ) 2) :2+ 2 + 2 = ( + )22 - 2 + 2 = ( - )2 2141:N : x2 - 6x + 8 = 0 x2 - 6x + 8 = 0 4x2 - 24x + 32 = 0 (2x)2 -2 2x 6 = -32 (2x)2-2 2x 6 + 62 = 62 - 32 (2x + 6)2= 4 . () ()1. x2 + x + = 0 2 .2. x-2 + x + =0 0 2 .3. x2 - x = 0 .4. x2 - 4x = 0 x = 4.5. A 2 .6. 2 .7. x2 + x + = 0 0 1 + + = 0 8. H x2 - 2007 = 0 . 1. ) 3x2 - 27 = 0 ) 4x2 - 16 = 0 ) x2 - 5 = 0 ) x2 - 9 = 0 ) x2 - 5 = 0 2142. . x2 + x + = 0 0 : x2 + x + = 0 4 x2 + 4 x + 4 = 0 42x2+ 4x + 4 = 0 (2x)2 + 2 2x = -4 (2x)2 + 2 2x + 2 = 2 - 4 (2x + )2 = 2 - 4 . 2 - 4 , :(2x + )2 = : A >0, : (2x+)2= 2x+= 2x=- x=2 . x=2 + x=2 A =0, : (2x+)2=02x+=0x=-2 . x = -2

= 2 - 4 x2 + x + = 0, 0 : >0 x1,2=2 A=0 0 . , x=2 =3 21 ) 4 ( = =21 4 , x=21 4 + =25, x=21 4 =23 . ) =-2, =-4, =6 =2-4=(-4)2-4(-2)(6)= 16+48=64 >0 . , x=2 =) 2 ( 26 4 ) 4 ( = =48 4, x=48 4+=-3, x=48 4=1 2 : A x2 + x + x2 + x + = 0 (1) :1. > 0 (1) 1, 1 x2+ x + = (x- 1)(x- 2)2. A = 0 (1) x=-2 x2+x+=(x+2)2 3. A < 0 (1) . 2144 .E () ()1. x2 + x + = 0 0 .2. 3x - x2+ 1 = 0 = -11.3. x2 + x + = 0, 0 , .4. x2 - x = 0 .5. 2 < 0 6. = 0 > 0 x2 + x + = 0 .7. x2 - 4x = 0 x = 4.8. A 2 .9. 2 .10. x2 + x + = 0 0 1 + + = 0 11. x2 + x + = 0 0 0 = 0 12. 2 .13. 1, x2 -4x + - 1 = 0 0.14. x2 -4x + -5 =0 = 9 15. x2 -x - =0, 0, R.16. x2 + x + 0 . 2145. 1. x2-3x + 42 = 0 0 :. . . . .2. x(x2- 1) = 0 :. 0, 1, -1 . 0, 1 . 0, -1 . 3. x2 - x + = 0 , :. x2 - x - = 0, . x2 + x + = 0 . x2 - x + 1 = 0, 0. x2 + x - 1 = 0 0 4. x2 - 4x + 4 = 0 :. < 1 . > 1 . > 3 . 1 5. A x2 - 6x + = 0 :. 9 . 8 . -9 . -8 6. A 1, 2 : x2 + x + = 0 0 x2 + x + :. (x- 1)(x- 2) . (x- 1)(x- 2) . (x- 1)(x- 2) 1. ) 3x2 - 27 = 0 ) 4x2 - 16 = 0 ) x2 - 5 = 0 ) x2 - 9 = 0 ) x2 - 1 = 0 ) x2 + 6 = 0 ) x2 + 8 = 0 ) 3x2 + 48 = 02. N ) 3x2 - 2x = 0 ) 16x - x2 = 0 )2x2 - 4x =0 ) -x2 = x ) x2 = x ) 3x2 = 6x ) x = 2x2) 7x = -14x23. N ) 3x2 - 1 = 2(x2 + 12) ) 3x2 - 4x = -8x ) (x-2)(x + 2) + (1- 2x)(1+ 2x) = 0 )x2 = 10x + 25 ) 7x = x2 - 18 ) x2 = x-1 ) 3x2= 2x - 4 4. N ) (2x - 3)2 = (x - 1)(x + 4) + x ) 9(2-2) - 8 = 4(2 -1) + 14 ) ( + 2)(7 - 1) = (4 + 5)(5 - 3) )-(3x -1)2 = (4x - 1) 21464. N ) (2x-3)2 = (x-1)(x+4) +9x) 9(2-2) -8 = 4(2-1)+14 ) (+2)(7-1) = (4+5)(5-3)) 47-(3x-1)2= 23(4x-1)5. ) 22) 2 (4131 2+ =+++xx x) 21624) 1 (3) 2 (2++=++ x x x x x )3) 1 ( 242952x x x =+)xx x x+=++412151 42 2 ) 22) 2 (4131 2+ =+++xx x) 21624) 1 (3) 2 (2++=++ x x x x x )3) 1 ( 242952x x x =+)xx x x+=++412151 42 2 6. ) x3 - 5x2 - 6x = 0 ) x3 = 2x2 + 3x ) x2(x -2) -2x(2 -x) + x -2 = 0 ) x2 (3 -x) + x(x -3) + 6(x -3) = 0 ) (x + 2)3 + x2 - 4 = 0 7. N ) x2+(2 2 +3)x+3 2 +4 =0 ) x2+( 1 5 ) 3 5 + + x=0)2 x2-( 6 ) 2 6 + + x=0 ) 0 1 2 32= x x8. )-2x2+4,6x-2,4 =0 ) 0,002x2+4,004x-1,01=0) x- x-20 =0 )x-3 x +2 =0)9. 3x2 - 2x + 4 = 0. ) ) ) .10. x2 - 3x + 2 + 7 = 0 -2.11. (x + )2 -2( - x) = 7. N 2; 12. A x2 - 3x - 5 = 0 = 2 - 3 = 2 - 3 + 10 x4 - 3x2 + 2 = 0 214713. R, x2 - 2x + 2 = 0 2. .14. R :(2 - 3 + 2)x2 + 3x - 2007 = 0 2 .15. N : x2 - 6x - 34 = 0 (1) (1) 16. : x2 - x + 2 = 0 (1) (1) 17. .) 6x2-x-1 ) x2-x-2 ) 2x2-x-1) 4x2-4x+1) 31x2-2x+3) 2x2+4x+3 ) 3x2-4x+118. : A=22 322 + x xx x,B =1 22 322 3 + x xx x x = 2 61 4 19 322 +x xx x 19. x2 - 4x + -1. :) .) .) .20. N :) x3 - 6x2 + 5x =0 ) x4+ 5x3- 6x2 = 0 2148 2.3 1. x + 1. A 7-x x. N x.2. ) 6 , . .) :10 , 20 .) 465 , .3. 5 cm . 12 cm2, .4. : 5. 2 cm 152 cm3. .6. . 110cm, .7. 4000 90 . , . 21498. 24 m, 0 = 2m/sec . ;9. A , 42. .10. (x) = 90 + 2x x . (x) = x2 - 18x - 210 P(x). , .11. (t) = t3 - 5t2 + 4t ) t = 2 sec ) t = 0 12. . 4 cm, 9 cm , . 2150 2.4 K . . : ... . . . ... . . . 1. :) :T ... ... = (x - 2)(x + 2) .:(x - 2)(x + 2) 0 x - 2 0 x + 2 0 x 2 x -2. : 2151) ... x2(x + 1)2 .: x2(x + 1)2 0x 2 0 (x + 1)2 0x 0 x -1 . () ()1. 1. 2. x2 - 4 = 0 .3. .4. 0 . .1. :. 0 2, . 0, 2 -2 . 0 -2 . 2 -2 2. :. -1, . 0, . 0, 1, -1 . . 3. H :. 1 . -2 . -1 . -1 -2 2152 1. R :2. Q :3. :4. , x2 - 5x + 6 = 0.5. , 4 . 6. 12 7. T 120 . 3 , 9 , . .8. , , 3 . . .9. 5 . 180 , 80 . , 4 . 215310. 300 m . 5 m / h, 300 m 2 h . ; 2.5 - , :) > - > 0.) O < -< 0.) - - = 0 .1. .2. 0 .3. 0 .4. . , , . : - > 0 > - < 0 < - = 0 = 1. . : A > ) + > + ) - > - 2154) + , + . : + - ( + ) = + - - = - . > , - >0. ( + ) - ( + ) , + > + ) - , - . : - - ( - ) = - - + = - . > , - > 0. ( - ) - ( - ) , - > - 2. . : A > > 0 ) > )) , . : - = ( - ) (1) . > 0 - > 0, > . - , , ( - )>0 . (1) - , > ) . :(1) . > 0 - > 0, > . - , , , (1) , 3. . : A > < 0 < 4. , . 2155 : > > + > + :A > > > 5. , . :A , , , > > > > > 0, 2) > (1) > > 0, > (2), (1) (2) > . :) .) .) .) ) 2 0 .:A , 2 + 2 = 0, = 0 = 0 . ) .) .) . 2156 1. x < 2, :) 3 (x - 2) 2(x - 4)) 2(3- ) 3(-x +5) +2x) 0.3(x - 2) -2(x - 2) = 3x -6 -2x + 4 = x -2 < 0 x < 2 . 3(x - 2) < 2(x - 4)) 0. 2(3 - )-[3(-x + 5) +2x] = 6 -2 + 3x - 15 - 2x = -9 + x -2 , :) > 0, ( ;)) -22 -4 < -2x -2 (1). E3 -4 -45 -20 -4 < -12 (2). (1) (2) :3 - 20 3x -20 < 6 -12 -17 3x -20 < -6 . 4. : )(x + 1)2 - (x - 1)2 < 0 x2+ 2x + 1 -(x2- 2x + 1) < 0 x2 + 2x + 1 -x2 + 2x -1 < 0 4x < 0 x < 0 . 2158 . () ()1. > > 2. > -2 x > x > -23. > > > 4. > > ->-5. 0x > 3 3 6. 2 > 0 > 0 7. 3>0 > 0 8. < 1 < 1 < 1 9. < , 2 > 212. > 0, , .13. > > , > 14. +x > + , > 15. > + + 16. o x 5, x 5 17. A x 8 x 8 18. x 5 x < 5 19. H -2x > -5x x. 215920. H 0 x < 3 .21. A x > 1 2x-1 < 0 22. A x > 0 x > 2x 23. A x< 0 x > 2x 24. A < < 0 2 > 225. < 0 > 026. < 0 0 < 0 . 1. -2x < 4 :. 0, -2 . -2 . -2. 2. , o -3x > -7: . -2 . 2 . 0 . 1 . -13. x < 1 :. 1 + x < 2 . x-2 < -1 . 3-x> 2 . 3x< 3 . x2 < 1. 4. A x( - 1) 0, .. = 1 . < 0 . < 1 . > 0 . > 1 5. = N* :.111. 1 + < 21 2160 1. 1< x < 2, :) (1-x)(x-2) (x+3) x ) (x+2)(x-21) (x-3) (2-x)2. < , :) 5-5x5 -5x) 54 3+ x 54 3+ x 3. , > > , :) ( - )( - )(2 -) > 0 ) 3 - + > 2 + 4. : 0 < < , :),1)1 + + , +15. 0 < x < 1 -2 < 83 -61(4x-12))7(2x-3)-41 ) 2 ( 3 x > 3x -2

) 62 3 x > 41 2 x )41 x< 25 3 x 8. :) 43 x-x < 21 x -32 x2-x > 2x-8) (x + 1)2 > x(x + 1) 4x(x - 1) (2x - 1)29. : 216110. x, :) x-1 2(1-2x) < 4-x) 42 3 + x x-1 32 x 11. N , 41 2

-2 3.12. :5x - xx x+>25 722 3 (1) 425 232 7 < xxx (2)13. :) 3x + 4 = 2(x - 3) 3(2x - 4) 3 - 5(5 - x) ) (4x - 1)(x - 3) = 0 3x - 7 -4x 14. ) x 14,6 -1 02 2 06 , 111 02 5 x x < ) x 412 32 423 >+ x x x15. T 12 17. .16. 8 53.17. 10 .18. 20 . 35 . 500 10 .19. : 30 . 8 . 7 , . ;20. = 3x -5. N x ) 10 ) 5 ) 0 ) . 2162 2 1 To :) : 105. ) 10.) x+x+1+x+2++x+10 = 66 x .2 x = - 5, .) .) .3T = x, A =x + 2 = 10. (x + 2)2 - x2 = 28, = 90.4 , : 2 + 2 + 2 + 4 + 5 = 0. 10 1. ) ;) ;) ;) ;. ) : x2 - 4x = -3. (1) ) () . 2 ) x .) : 2163 3 :) ) 4 : x2 - 4x + 42 - 1 = 0(1)) (1) ) 1, 2 (1) -1< 1 3 -1< 2 3.20 1. ) .) 2 , ) 2 . ) ) 2 1 x 4 3 7, : 3 :3x + 6 = 9 (1), x2 - 4x + 3 = 0 (2)) 2164) ) (2). 4) ) 3000 . 1800 3 . 100 , . 100 . 2 2.1 x + = 0 1. 1 3 2 1 2.) ) ) ) ) 1. ) -3(x + 2) - 2(x - 1) = 8 + x -3x -6 -2x + 2 = 8 + x -3x -2x -x = 8 + 6 -2 -6x = 12 x = -2 )4 -2( -3) = 2 + 1 4 -2 + 6 = 2 + 1 4 -2 -2 = 1 - 6 0 =-5 )5(- +2) -4 = 6 -5 -5 + 10 -4 = 6 -5 -5 + 5 = 6 - 10 + 4 0 = 0 2165 2. ) 0,2(3x - 4) -5(x - 0,4) = 0,4(1 - 10x) 0,6x -0,8 -5x + 2 = 0,4-4x 0,6x -5x +4x = 0,8 -2 +0,4 - 0,4x =-0,8 x = 2 3. 4. 5. x : .6. x , x-1 . 16x + 12(x - 1) = 44 16x + 12x - 12 = 44 28x = 44 + 12 28x = 56 x = 2 .( 21662.2E 2 1.) ) ) ) ) ) 2.) ) ) 3. x x 0. 1. 2. 21673. 4. 5. 21686. 7. 8. : :1. 12 , 151. 10 2. 0 , 322. 153. 10, 13. 30 4. 25, 32 4. 12 5. 12 1. 2 3 1 42.) ) ) 3. ) ) 2169 1. x2+x+ = 0 x(x-1) = -2x2 -x + 2 = 0 1 -1 23x2+ 4 = 2(x + 2)3x2 -2x +0 = 0 3 -2 0(x-1)2 = 2(x2- x) -x2 + 0x +1 = 0 -1 0 12. 21703. 4. 2171 5. 21726.7.8. 2173 1. 2. 21743. 4. 5. 6. 7. 21758.9. 10. 11.12. 217613. 2.4 H O.1.) ) ) ) 2. )3. )4. x = 1 . 1. 2177 2. 2178 3. 2179 4. 2180 5. 2181 7.6. 2182 8.9.10. 218312. 11. 21842.5 E 1.) ) ) ) ) ) ) ) 2.) -3>0, ) < , ) ) 2 > 0 ) + 0 3. 4 3. 4. ) 4 ) 2 .) 5. ) -6 5. ), )6. , , . - 1. 3( - ) >2( + ) 3 -3 >2 + 2 3 - 2> 3 + 2 > 52.)x>-6 ( -5)-5x < 30 ( -30)-5x - 30 < 30 - 30 -5x - 30 < 0 )x >- 6( 3) 3x > -18( 18) 3x + 18> -18 + 18 3x + 18 > 0 )x > -6 ( 4) x + 4 > -6 + 4x + 4 > -2( 2) 2(x + 4) > -4.3. ) : 2 < < 6 2 : 0< -2 < 4 ) : 2 < < 6 2 : 4 < 2 < 12, 5 -1 < 2 -5< 7 ) : 2 < -3 > -18-18 < -3 < -6, 1 : -17 < 1- 3 < -5 21854. ) < 5 0 ) x + 2, (x + 2) > 12 7. > - >0. + , - , ( + )( - ) > 0 2- 2>0 2>2.8. ) >1 (1), > 0. > 1 2> .) x > 2 (1), x >0. x2 x2 x > 2 x2 x3 > 2x29. >0 :.10. ) x > 3 x - 3 > 0, < 2 - 2 < 0. x - 3, - 2 , (x - 3)( - 2) < 0.) ) (x - 3)( - 2) < 0 x - 2x - 3 + 6 < 0 x + 6 < 2x + 311. )x2+ 1 2x x2- 2x + 1 0 (x - 1)20. . x - 1 = 0 x = 1. ) (x + )2- 4x . 2186(x + )2 - 4x =x2 + 2 + 2x - 4x = x2 + 2 - 2x = (x - )2 0. . x - = 0 x = .) x2 + 2 + 1 - 2 . x2+ 2+ 1 -2 =x2+(-1)20. . x = 0 -1 = 0 x = 0 = 1. 12. ) .. : (x - 1)20 x>0) ( ) . : (x - 1)20 x 20 + 15 0x> 35 . 2187) ) ) 17. )7x - 1 < 8 + 6x 7x - 6x < 8 + 1 x < 9 3x - 2 > x - 10 3x - x > -10 + 2 2x > -8 x > -4 -4 < x < 9 )4x + 3 < 9 + 5x 4x - 5x < 9 - 3 x < 6 x > -6 1 - x < 2x + 7 -x - 2x < 7 - 1 -3x < 6 x>-2. x > -2.) x < -2 18. 2188 2 1. )(x + )2 - (x + )2 = 2 - 2 x2+ 2x + 2 -(x2 + 2x + 2) = 2- 2x2 + 2x + 2 - x2 - 2x - 2 = 2 - 2 2x - 2x = 2(2 - 2) 2(-) = ( - )( + ). ) ... 0, (x+) (x + )= 2 - x + 2 x-2-x - 2 = 2- (-)x == 2- . 2. 2 = 2 + 2, (x + 2)2 = x2+ (x+1)2 x2 + 4x + 4 = x2 + x2 + 2x + 1 x2 - 2x - 3 = 0. = 1, = -2, = -3. = 2 - 4 = (-2)2 - 4 1 (-3) = 4 + 12 = 16 > 0. x = 1 B = 1 + 2 = 3, : 2 = 2 + 2, (3-2)2 = 52 +(2 + 2)2 92- 12 + 4 = 25+ 42+ 8 + 4 52- 20-25 = 0 2-4-5 = 0 = 1, = -4, = -5. = 2-4 = (-4)2-41(-5) = 16 + 20 = 36 >0 3. x x + 1. x(x + 1) = (x + x + 1) 7 = 23 x2+ x = (2x + 1) 7 + 23 x2+ x = 14x + 7 + 23 x2- 13x - 30 = 0 = 1, = -13, = -30. = 2- 4 = (-13)2 - 4 1(-30) = 169 + 120 = 289 > 0 21894. ) x - 0 x + 0 x x -... (x - )(x + ) 0, = 3, = -, = -22. = 2 - 4 = (-)2 - 43(-22) = 2 + 242 = 252 > 0 ) x 0 x + 0 x - 0 x 0 x - x .... x(x - )(x + ) 0, 3(x + ) + x - = 6x2 3x + 32+ x - = 6x2 6x2-(3 + 1)x - 32+ = 0 = 6, = -(3 + 1), = -32 + . = 2 - 4 =[-(3 + 1)]2 - 4 6 (-32 + ) = (3 + 1)2 - 24(-32 + ) = 92 + 6 + 1 + 722 - 24 = 812 -18 +1= (9 - 1)2 0 21905. 1 12 + ( - 5) 1 + = 0 1 + - 5 + = 0 2 = 4 = 2. = 2 : x2 - 3x + 2 = 0. = 1, = -3, = 2. = 2 - 4 = (-3)2 - 4 1 2 = 9 - 8 = 1 >0 x = 2. 6.K (x): (x - 3)

x-3x3+3x2-13x-15 -x3+3x2 6x2-13x-15 -6x2+18x 5x-15 -5x+15 0 x2+6x+5 A x3 + 3x2 - 13x - 15 = (x - 3)(x2 + 6x + 5). (x) = 0(x-3)(x2 + 6x + 5) = 0 x - 3 = 0 x2 + 6x + 5 = 0 x = 3 x2 + 6x + 5 = 0. = 1, = 6, = 5. = 2 - 4 = 62 - 4 1 5 = 36 - 20 = 16 > 0. x = = 2 1 216 6 = 24 6 . x = 24 6

= -5 x = 24 6 + = -17. x, x+1 ( , ). x1+ 11+ x +x1 11+ x= 1. ... x(x+1) 0, x(x+1) x1+ x(x+1) 11+ x+ x(x+1) x1 11+ x =x(x+1) (x+1)+x+1 = x2+x x2-x-2 = 0. = 1, = -1, = -2. = 2-4 =(-1)2-41(-2) = 1+8 = 9 >0. x = 2 = 1 29 ) 1 ( = = 23 1, x = 23 1+ = 2 x =23 1 = -1 . 8. x > 0 x + 2 x(x + 2) = 399 x2+2x-399 = 0. = 1, = 2, = -399. = 2 - 4 = 22-4 1 (-399) = 4 + 1596 = 1600 > 0. x = 2 = 1 21600 2 = 2191240 2 , x =240 2 = -21 . x = 240 2 + = 19. : 19, 21 9. 2 + 2 = 2 (1). : 2 = 2+ 2 2 = 32+ x2 2 = 9 + x2. :A2 = 2+ 2 A2 = x2+(2x+9)2 = x2 + 4x2 + 36x + 81 = 5x2 + 36x + 81. B2 = (2x + 12)2 = 4x2 + 48x + 144. (1) 5x2 + 36x+ 81 + 9 + x2 = 4x2 + 48x + 144 2x2- 12x - 54 = 0x2- 6x - 27= 0. = 1, = -6, = -27. = 2 - 4 = (-6)2 - 41(-27) = 36 + 108 = 144 > 0

x = 2 = 1 2144 ) 6 ( = 212 6 x =212 6 + = 9 x = 212 6 =-3 .10. .(1 + )(1 + ) - (1 + + ) = 1 + + + - 1 - - = ) A = 0 (1+)(1+)=1++) A > 0 (1+)(1+)>1++) A < 0 (1+)(1+) 0 .(+1)(+2)) 2 (4+ v - (+1)(+2)) 2 ) ( 1 (1+ + > (+1)(+2)) 1 (2+ 4(+1)->2(+2) >0 4+4->2+4 >0 . 13. ) 2 + 2 > 2 - 2 2+ 2 - 2 + 2 > 0 ( + )2 - 2 > 0 ( + - )( + + ) > 0. : + > + - > 0 + + > 0 ( )) 2 + 2 < 2 + 2 2 + 2 - 2 - 2 < 0 ( - )2 - 2 < 0 ( - - )( - + ) < 0.(1) : < + --< 0 + > + - > 0, (1) .) ) 2+ 2 < 2 + 2 (1), 2 + 2 < 2 + 2 (2), 2 + 2 < 2 + 2(3). (1), (2), (3) : 21922 + 2 + 2 + 2 + 2 + 2 < 2 + 2 + 2 + 2 + 2 + 2 2 + 2 + 2 + 2 + 2 + 2 - 2 - 2 - 2< 2 + 2 + 2 2 + 2 + 2 < 2 + 2 + 214. 2007 = 2008 = 2009= > 0, 2007 = , 2008 = , 2009 = , = 2007, = 2008, = 2009, 4, .16. 2 + 2 + 2 - 2 - 4 - 6 + 14 = 0 2 - 2 + 1 + 2 - 4 + 4 + 2 - 6 + 9 = 0 (-1)2 + ( - 2)2 + ( - 3)2 = 0, - 1 = 0 - 2 = 0 - 3 = 0 = 1 = 2 = 3. 17. = 2 - 10 + 2722 - 8 + 8 = 2 - 10 + 252 + 22 - 8 + 8 = = ( - 5)2 + 2(2 - 4 + 4) = ( - 5)2 + 2( - 2)2. E ( - 5)2 0 2( - 2)2 0 0. 0. - 5 = 0 - 2 = 0 = 5 = 2 = 10 = 2 18. : x - 19 = (x-2020) + 2001, x - 17 = (x - 2020) + 2003, x - 15 = (x - 2020) + 2005, x - 13 = (x - 2020) + 2007. O200119 x+200317 x+200515 x+200713 x = 4 20012001 2020+ x+20032003 2020+ x+20052005 2020+ x+20072007 2020+ x = 4 20012020 x+1+20032020 x+1+20052020 x+1+20072020 x+1 = 4 (x-2020)(20011+20031+20051+20071) = 0 x-2020 = 0 x = 2020. 19.1. 1. 2. .2. 3. 3. 4. 4. 5. 5. 6. 6. 7. 3 3195 3.1 x + = 0, x , R , , = R.T x, , , . . x + = (x,) .:)A , .) . =, 0 o xx (0,), = 0 xx.H x = 0 xx (,0) , x = 0 . x (x,0) (0,): () :) xx, = 0 x.) , x = 0 . 3196 1 : 7x + 2 = 9. .(1,1) ( 3,-2) (0,0) :7 1 + 2 1 = 7 + 2 = 9, : 7 3 + 2 (-2) = 21 - 4 = 17 9, : 7 0 + 2 0 = 0 9, 2 2x + 3 = 5 ) (1 , 1) (-2 , 3) ) ) ( -1,)) : 2 1 + 3 1 = 2 + 3 = 5, . : 2 (-2) + 3 3 - = 4 + 9 = 5, B ) x = 0, =35, :(0,35) = 0, x =25,2535 (25,0)) 2 ( - 1) + 3 = 5 2 - 2 + 3 = 5 5 = 5 + 2 5 = 7 =57 . 3 () 4x + 6 = 12.) () ) () xx, () .) xx: 0, 4 x + 6 0 = 12 4x = 12 x=3 xx (3,0) : x 0, 4 0 + 6 = 12 = 2. (0,2 ) ) ) (3,0) x = 3 31974 : (2 - 1)x + ( - 1) = 3 (1) ) (1) .) (1) xx.) (1) (0,3).) x + = , , . x . - 1 = 0 = 1. (1) =1 : 12 - 1 = 0, = 1 .) (1) xx :2 - 1 = 0 ( - 1)( + 1) = 0 - 1 = 0 + 1 = 0 = 1 ( ) = -1 . = 1 = 1 . ) (1) (0,3) (2 - 1) 0 + ( - 1) 3 = 0 3( - 1) = 0 - 1 = 0 = 1 . (1) (0,3)E . () ()1. 3x2 + =7 .2.H +x = .3. (-1)x+(2-1) = 3 .4. x = 5 .5. = 6 .6. x = 5 x = -1 .7. = 3 x = -4 .8. x = 3 x. 31989. (2 - 1)x + ( - 1) = 0 .10. .11. =6 .12. 3x 5 = 0 .13. (x0, 0) x + = x0 + 0 = .14. x + = .15. 3x + = 3 .16. (-1,2) x = 2. 17. = x .18. () 3x-=3 () x- =-1 (0,0). 19. : 2x + 2 = 6 xx (-3,0). 20. x = 4 = -2 (4,-2).21. x = 5 (0,5).22. 2x + 6 =0, ..N :1. = 6 :. xx . . = 3 . = 6x.2. A () 3x - ( - 1) = 3 (, ) :. = 1 . = 0 . = 1 = 3 .3. To () 2x - = 1 () 3x + 2 = 5 :. (0,0), . (1,1), . (-1,1) . (1,-1)4. (-2,3) :. x = -2, . x = 2,. = 3, . = 2 31995. H () 2x + 4 - 8 = 0, xx :. (4,0), . (0,4),. (2,0), . (0,2). 6.H x = 4 :. xx, . , . = x, . = -x. 7. :. 2x - x = 2, . 4x - 5 + 3 = 0 . x - 1 + = 3, . x + - 1 + 2 = 0 8. (2 - )x + = 3. :. = 0, . 0, . 1, . = 19. : x -4 = 8, :. 8 .., . 4 . ., . 2 . ., . 16 ..A 1. :) 1: x - 3 =4 ) 2: x - = 0, ) 3: x = 4 ) = -2 2. (): 3x - = 3.) x/x (2- 3 ,0). ) ) : x + = 5 3. (): x - 4 = 8 ) () .) () x / x, / .4. (): x + 5 = 10. : ) xx 2. ) ) () .5. , (2 - 1)x + ( - 1) = 3 ) ) xx) 32006. (2 - 2)x + ( - 2) + 2 - 4 = 0. :) ) .7. : 4x + (2 - 3 + 2)x + 2 - 6 = 0. . :2x - + 4 = 0. 3.2 x , .: x (x,) . x, . : : A . , . . 3201 1 ) ():-23x=03x+2=6 ) 1 : 3x+2=6 ,2 : -23x=0 o . ) . (1,23) . (x,)= (1,23) ) 3 23. : E= 21 =213 23 =49 .2 :x+2 =4x=5 =4x-5 =0 )) ) ) 3x-5 =1x+=0 x=-7 +3=0) . 3202 ()81 1,45 (x,)= (45,81 1)) . (5, -5) (x, ) = (5, -5) ) 3203 (-7, 4) (x, ) = (-7, 4) ) (5, -3) (x, ) = (5, -3) . () ()1. . xx.2. , .3. x, .4. : x = 3 x - 5 =0 .5. : 3x - 6 = 0 - 4 = 0 .6. 3x + 2 = 1, 3x - 5 = 6 . 32047. T (-1,3) :x+3=1x+2=5 8. x+=8 x+2=10. :1. (1,1) (-2,-2) :. = x, . = 3x - 1, . = 3x - 2, . = x + 1 2. + 2x = 4 xx :. (2,0), . (0,2), . (0,4) . (4,0)3. : () 2x - 5 = -3, ()x + = 2. , . , . . .4. : () 2x - = 0,3x + = 0 :. (0,0), . (1,2), . (1,-3), . (-3,1) 1 : () 3x + 2 = 5, ()x + 2 = 1.) :) () 4x - 3 = 1 .2 : () x - 4 = 8 ) ) () .) () (-2,3) xx.3 : () 3x - = 3,() x- 2 = 4() 2x - = 2 ) () .) (), () .) . 3205 3.3 , . , . .) : : . , , . , . .) : : , .