ГДЗ - алгебра - 9 класс - Макарычев

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  • 21.) f(1)=3(1)2+10=7;) f(0)=3+10=302+10=10;

    ) f(31 )=3(

    31 )2+10=3

    91 +10=

    329 .

    2.

    ) f(0)=5,005,00

    +

    = 15,05,0

    =

    ;

    ) f(1,5)=21

    5,05,15,05,1=

    +

    ;

    ) f(1)= 35,05,1

    5,015,01

    =

    =

    +

    .

    3.) f(5)=5310=12510=115.) f(4)=4310=6410=54.) f(2)=2310=810=2.) f(3)=(33)10=2710=37.

    4.1) (0)=02+0+1=1;2) (1)=12+1+1=3;3) (2)=22+2+1=4+2+1=7;4) (3)=32+3+1=9+3+1=13;

    (0)+(1)+(2)+(3)=02+0+1+12+1+1+22+2+1+32+3+1=1+3+7+13=24.

    5.

    ) 5x+6=17; -5x=176; x=5

    11

    =2,2.

    ) 5x+6=3; 5x=6+3; 5x=9; x=154 .

    ) 5x+6=0; 5x=6; x=151 .

    6.) x(x+4)=0; x1=0, x+4=0; x2=4.

    ) x

    x

    +

    51 =0;

    =+

    0501

    xx

    ; x=1.

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  • 37.

    ) x+6

    4 =1;4=1(6+x); 4-6=x; x=2.

    ) x+6

    4 =0,5; 4=-0,5(6+x); 8=6x; x=14.

    ) x+6

    4 =0; 4=(6+x)0; 4=0; .

    8.

    ) 0,5x4=5, 0,5x=1, x=5,0

    1 , x=2.

    ) 0,5x4=0, 0,5x=4, 5,0

    4=x , x=8.

    ) 0,5x4=2,5, 0,5x=6,5, 5,05,6

    =x , x=13.

    9.) .) .) 5x0, x5. , 5.) (4)(+1)0; x40; x4 x+10; x1.

    , x=5; x=1.) x2+1=0 . .) 50; 5. : 5.10.

    ) y=10x; ) y=355

    6x

    11.) .) 1+x0; x1. x=1.) 9+x0; 9. x9.

    12.) g(4)=3; g(1)2; g(1)=3; g(5)=3;) g()= 1,3, 4,4; g()=4 =3; g()=0 =5, =0;) 6 =3; - 4 =3.) : [4; 6].

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  • 413.) D(f)=(; ); E(f)=(; ).) D(f)=(; ); E(f)=(; ).

    ) D(f)=(; 0) (0; ); E(f)=(; 0)(0; ).) D(f)=(; 0) (0; ); E(f)=(; 0)(0; ).

    14.1) y=x2: D(y)=R, E(y)=[0;+].2) y=x3: D(y)=R, E(y)=R.3) y= x : D(y)=[0:+), E(y)=[0;+).

    15.) y=

    x2 ; ) y=

    x2 ; ) y=

    2x ; ) y=

    2x2; ) =2

    2x .

    16.

    x=0 y=1, x=21 y=0, ,

    y=2x1.

    17.) |x|=3,5 =3,5 x=3,5; ) |x|

  • 518.) E(f)=(8; 8); [3; 3]

    x3 2 1 0 1 2 3

    y3 8 7 0 7 8 3

    ) E(f)=(0,5; 8); x[1,5; 6]x

    1,5 1 0 1 3 4 5 6y 8 4 2

    34

    54

    32

    74

    21

    19.(20)=220+20=60; (40)=100; (50)=100;

    (60)=3260+140=40+140=100; (90)=

    32 90+140=60+140=80.

    [0, 40] , [40; 60] , [60; 150] .

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  • 620.s(0)=150=0; s(1)=151=15; s(1,4)=17,5; s(2)=122+35,524=11,5.

    1 10 , 20 -, 1 .

    21.) 0,5(3x4)+15x=4(1,5x+1)+3; 1,5x+2+15x=6x+4+3; 7,5=5;

    = =5,7

    532 .

    ) (2x3)(2x+3)x2=12x69+3x2; 4x26x+6x9x2=12x69+3x2;4x2x23x212x=969; 12x=60; x=5.

    22.

    ) 6x23x=0; 3x(2x1)=0; 3=0; x1=0 2x1=0; x2= 21 .

    ) x2+9x=0; x(x+9)=0; x1=0, +9=0; x2=9.) x236=0; x2=36; x1,2= 36 ; 1=6; 2=6.) 5x2+1=0; 5x2=1; x2=

    51 . , ..

    .) 0,5x21=0; 0,5x2=1; x2=2; x1,2= 2 ; 2;2 21 == xx .

    ) 0,6x+9x2=0; x(0,6+9x)=0; x2=0; 9+0,6=0; 96,0

    =x ; x1= 151 .

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  • 723.

    ) x2+7x+12=0; D=724112=1; x1,2= 217

    1217 =

    ; x1=4,

    x2=3.

    ) x22x35=0; D=(2)241(35)=144; x1,2= 2122 x1=5, x2=7.

    ) 2x25x3=0; D=(5)242(3)=49; x1,2= 475 , x1= 2

    1 , x2=3.

    ) 3x28x+5=0; D=(8)2435=4; x1,2= 628 , x1=1, x2=1 3

    2 .

    24.) [0;6];) [14;16];) [6;14].

    25. 0 13 20

    100, 70 13 28 . 28 . 100.

    26.) f(x)=0 x=5; 3; 1; 4.) f(x)>0 7x

  • 829.

    ) )

    30.

    )

    03 3

    y

    x

    )

    04 2

    y

    x

    ) 03 2

    y

    x1 5

    31.

    ) 0,8x+12=0; 0,8x=12; 158,0

    12=

    =x .

    ) (3x10)(x+6)=0; 3x10=0, x+6=0; .. x1=3 31 ; x=6.

    ) 4+2x=0 x2+50; 2x=4; x=2.) .

    32.

    ) 2,1x70=0 (x=3331 ), ,

    .) 4x(x2)=0 2 (x=0 x=2), ,

    .

    ) x

    x6 =0 (x=6), -

    , .

    33.) f(x)=0,7x+350

    1) f(x)=0 0,7x+350=0; 0,7x=350;

    5007,0

    350=

    =x .

    2) f(x)>0 0,7x+350>0; 0,7x+350>0;

    0,7x>350; x

  • 93) f(x)0; 30>10; > =3010

    31 .

    3) f(x)2.

    3) y

  • 10

    1) y=0 0,6x+5=0; 0,6x=5; x= =

    6,05 8

    31 .

    2) y>0 0,6x+5>0; 0,6x>5; 0 x>03) y78; x> ;1378 x>6.

    ) f(x)0; y0 x0;

    x>0 x

  • 11

    39.

    ) y=x3

    1) x0 ;2) k=3>0 y>0 >0;3) k=3>0 y

  • 12

    41.) g(2)=

    91

    541

    521

    2=

    +=

    +; g(2)=

    91

    541

    5)2(12

    =

    +=

    + g(2)=g(2).

    ) g(2)=92

    522

    2 =+; g(2)=

    92

    5)2(22

    =

    +

    ; .. g(2)>g(2).

    ) g(2)=92

    542

    522

    2=

    +

    =

    +

    ; g(2)=92

    542

    5)2()2(

    2=

    +=

    +

    ; .. g(2)

  • 13

    x1= =

    431 1, x2= 2

    142= .

    ) 2x2+12x18=0; x26x+9=0; D=(6)2419=0; x=2

    06+ =3.

    ) x22x4=0; D=(2)241(4)=20; x1,2=2

    202 ; x1=1 5 ,

    x2=1+ 5 .

    ) 12x212=0; 12(x21)=0; 21=0; 2=1; = 1 ; x1=1, x2=1.46.) D=(8)2453=4>0, .) D=62491=0, .) D=62472=200, .

    47.) D=1644(3)=64>0. D=(4)24(4)3=64>0; .) D=16443=320; .

    48.) x26x2=x22x3+32322=(x3)211) x2+5x+20=x2+2x2,5+(2,5)2(2,5)2+20=(x+2,5)2+13,75.) 2x24x+10=2(x22x+5)=2(x22x1+1212+5)=2(x1)2+8.

    ) 21 x2+x6=

    21 (x2+2x12)=

    21 (x2+21+121212)=

    21 (x+1)26,5.

    49.) x210x+10=x22x5+5252+10=(x5)215.

    ) x2+3x1=x2+2x49

    49

    23

    + 1=(x+23 )2

    413 .

    ) 3x2+6x3=3(x2+2x1)=3(x2+2x1+12121)=3(x+1)26.

    ) 41 x2x+2=

    41 (x24x+8)=

    41 (x22x2+2222+8)=

    41 (x2)2+1.

    50.) x26x+10=x22x3+3232+10=(x3)2+1>0.) 5x210x+5=5(x22x+1)=5(x1)20.) 2+20x100=(x220x+100)=(x10)20.

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  • 14

    ) 2x2+16x33=2(x28x+233 )=2(x22x4+4242+

    233 )=2((x4)2+

    +21 )=2(x4)210.2) x2+6x11=(x26x+11)=((x3)2+2)

  • 15

    56.

    ) f(x)=0 6

    15,0 x =0; 0,5x1=0, 0,5=1; = ;5,0

    1 x=2.

    ) f(x)>0 6

    15,0 x>0; 0,5x1>0, 0,5x>1, ;

    5,01

    >x x>2.

    ) f(x)

  • 16

    ) 61 x2+

    21 x+

    31 =0; x2+3x+2=0; D=32412=1; x1= 2

    13 =2,

    x2= 213+ =1.

    61 x2+

    21 x+

    31 =

    61 (x+2)(x+1).

    ) x212x+24=0; D=(12)24124=48; x1=2

    3412 =62 3 ,

    x2=2

    3412+ =6+2 3 . x212x+24=(x6+2 3 )(x62 3 ).

    ) y2+16y15=0; y216y+15=0; D=(16)24115=196;

    y1= 219616 =1, y2= 2

    19616 + =15. y2+16y15=(y1)(y15)=

    =(1y)(y15).

    ) x28x+9=0; x2+8x9=0; D=8241(9)=100; x1= 21008 =9,

    x2= 21008 + =1. x28x+9=(x+9) (x1) = (x+9) (1x).

    ) 2x25x+3=0; D=(5)2423=1; x1= 415 =1, x2= 4

    15+ =23 .

    2x25x+3=2(x23 )(x1)=2(x1)(x

    23 )=(x1)(2x3).

    ) 5y2+2y3=0; D=2245(3)=64; y1= 10642 + =

    53 , y2= 10

    642 =1.

    5y2+2y3=5(y 35

    )(y+1)=5(y+1)(y53 )= =(y+1)(5y3)

    ) 2x2+5x+7=0; 2x25x7=0; D=(5)242(7)=81; x1= 4815 =1,

    x2= 4815 + =

    27 . 2x2+5x+7=2(x+1) (x

    27 )=(x+1)(72x).

    61.

    ) 2x22x+21 =2(x2x+

    41 )=2(x22 x

    21 +

    41 )=2(x

    21 )2

    ) 9x2+12x4=(9x212x+4)=((32x)2223x+22)=(3x2)2.) 16a2+24a+9=((4a)2+234a+32)=(4a+3)2.) 0,25m22m+4=((0,5m)222m0,5+22)=(0,52)2.

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  • 17

    62.

    ) 2x2+12x14=0; x2+6x7; D=6241(7)=64; x1= 2646 =

    7, x2= 2646 + =1. 2x2+12x14=2 (+7) (x1).

    ) m2+5m6=0; m25m+6=0; D=(5)2416=1; m1= 215 =2,

    m2= 215+ =3. m2+5m6=(m2)(m3)=(2m)(m3).

    ) 3x2+5x2=0; D=5243(2)=49; x1= 675 =2, x2= 6

    75+ =31 .

    3x2+5x2=3(x+2)(x31 )=(x+2)(3x1).

    ) 6x213x+6=0; D=(13)2466=25; x1= 12513 =

    32 , x2= 12

    513+ =23 .

    6x213x+6=6(x32 ) (x

    23 )=(3x2) (2x3).

    63.) 10x2+19x2=0; D=192410(2)=441; x1=

    202119 =2,

    x2=20

    2119 + =0,1. 10x2+19x2=10(x0,1)(x+2).

    ) 0,5x25,5x+15=0; x211x+30=0; D=(11)24130=1; x1=2

    111 =5,

    x2=2

    111+ =6. 0,5x25,5x+15=0,5(x6)(x5).

    64.) 3y2+3y+11=0; D=324(3)11=141>0. .) 4b2 9b+7=0; D=(9)2447=310. .) 3y2 12y+12=0; D=(12)24312=0. .

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  • 18

    65.) 1) 3x2+2x1=0; D=2243(1)=16; x1=

    642 =1, x2=

    642 + =

    31 .

    3x2+2x1=3(x 13

    ) (x+1)= (x+1) (3x1).

    2) 13

    4)13)(1(

    )1(4123

    442

    =

    +

    +=

    +

    +

    xxxx

    xxx .

    ) 1) 2a25a3=0; D=5242(3)=49; a1=4

    75 =21 , a2=

    5 74+ =3;

    2a25a3=2(a+21 ) (a3) = (2a+1) (a3).

    2) 3

    12)3(3

    )3)(12(93

    352 2 +=

    +=

    aa

    aaa

    aa

    ) 1) b2b12=0; D=(1)241(12)=49; a1=2

    71 =3, a2=2

    71+ =4;

    b2b12= (b+3) (b4).

    2) ( )( )34

    )4)(3()4)(4(

    12162

    2

    +

    +=

    +

    +=

    bb

    bbbb

    bbb

    ) 1) 2y2+7y+3=0; D=72423=25; y1=4

    57 =3, y2=4

    57 + =21 ;

    2y2+7y+3=2 (y+3) (y+21 )= (y+3) (2y+1).

    2) 312

    )3)(3()12)(3(

    9372

    2

    2

    +=

    +

    ++=

    ++

    yy

    yyyy

    yyy .

    ) 1) p211p+10=0; D=(11)24110=81; p1=2

    911 =1,

    p2=2

    911+ =10; p211p+10= (p1) (p10).

    2) p2+8p+20=0; p28p20=0; D=(8)24(20)=144; p1=2128 =2,

    p2=2128+ =10; p2+8p+20= (p+2) (p10).

    21

    )2)(10()10)(1(

    82010112

    2

    +

    =

    +

    =

    +

    +

    pp

    pppp

    pppp .

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  • 19

    66.

    ) 1) x211+24=0; D=(11)24124=25; x1= 82511=

    + ,

    x2= 32511=

    .

    2) 83

    )8)(8()3)(8(

    642411

    2

    2

    +

    =

    +

    =

    +

    xx

    xxxx

    xxx

    ) 1) 2y2+9y5=0; D=9242(5)=121; y1=4

    119 =5,

    y2=4

    119+ =21 . 2y2+9y5=2 (y+5) (y

    21 )= (y+5) (2y1).

    2) 125

    )12)(12()12)(5(

    14592

    2

    2

    +

    +=

    +

    +=

    +

    yy

    yyyy

    yyy .

    67.

    ) 1) x27x+6=0; D