ГДЗ - алгебра - 10 класс -Алимов - 2001

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  • 10

    10-11 .. .,

    -.: , 2001.

  • 3

    I. .. 4 II. .. 37 III. .... 65 IV. .. 85 V. .... 123 VI. . 157 VII. .. 193

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  • 4 I. 1. 1) :

    0,2

    318 0,66

    ...20

    2) :0,8

    377 0,6630

    22

    ...30

    3) 6,0106

    5232

    53

    ==

    =

    4) 75,010075

    425325

    43

    =

    =

    5) 758

    7256

    728 =+=

    58

    756 8,285714220

    14

    6 6) 0,13

    9999 0,131

    310

    297

    ...31

    2. 1) 9929

    991118

    11911192

    91

    112

    =

    +=

    +=+ .

    0,29

    99198 0,292920

    891

    ...92

    , - : 6. ,

    == ...666,032 )6(,0 .

    , : 72.

    , 118 )72(,0...7272,0 == .

    , - : 285714. -

    , =728 8,2857142=8,( 285714).

    , : 13.

    , 9913 )13(,0...1313,0 == .

    , : 29.

    , 9929 )29(,0...2929,0 == .

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  • 52) 3950

    392624

    13313238

    32

    138

    =

    +=

    +=+ .

    50

    3939 1,282051

    110

    11

    3) 1219

    300475

    300375100

    100312531001

    100125

    3125,1

    31

    ==

    +=

    +=+=+ .

    19

    1212 1,58370

    60

    ...4

    4) 300149

    3009950

    5023333501

    10033

    6133,0

    61

    =

    +=

    +=+=+ .

    0,149

    3001200 0,49662900

    2700

    ...200

    5) 225,01000225

    2540259

    409

    455723753

    100105

    72305,1

    143

    ==

    ==

    =

    = .

    6) 90

    1191091777,1

    97

    =

    = .

    119

    9090 1,32290

    270

    ...203. 1) 0,(6). ...66,0)6(,0x == (1) . , -

    10, ...66,6x10 = (2)

    (2) (1), 6x9 = .

    , -

    : 282051. , =3950

    = )282051(,1...2820512,1 = .

    , : 3. -

    , =1219

    ...5833,1 )3(58,1= .

    , : 6. -

    , =300149

    ...4966,0 )6(49,0=

    , : 2. -

    , =90

    119...322,1 )2(3,1= .

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  • 6 32

    96x == .

    2) 1,(55). )55(,1x = =1,5555 (1) , ,

    ,100102 = ...55,155x100 = (2)

    (2) (1), 154x99 = .

    951

    914

    99154x === .

    3) 0,1(2) )2(1,0x = =0,1222. -

    , , 10, )2(,1x10 = (1)

    . , - 10,

    )2(,12x100 = (2)

    (2) (1), 11x90 = . 9011x = .

    4) 0,(8) )8(,0x = =0,888 (1) . , -

    10, )8(,8x10 = (2)

    (2) (1), 8x9 = . 98x = .

    5) 3,(27) )27(,3x = =3,2727 (1) . ,

    100102 = , )27(,327x100 = (2)

    (2) (1), 324x99 = .

    1133

    1136

    99324x === .

    6) 2,3(82) )82(3,2x = =2,38282 -

    , , 10, )82(,23x10 = (1)

    .

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  • 7, 100102 = , )82(,2382x1000 = (2)

    (2) (1), 2359x990 = .

    9903792

    9902359x == .

    4. 1) :3610045

    181002088)95,1159,19(:)36,0:4518:88,20(

    +

    =++

    =

    =

    +=

    +3154100

    18100227088

    1003154:

    122505045002088

    1001195

    1001959: 4.

    2) 7 11 9 5 7 11 9 5 79 8 9 836 32 10 18 4 9 4 8 2 5 2 9 4

    + + = + + = 4

    344

    1941

    411

    ==++ .

    5. 1) 4 3 2 79 4 24 215 23 0,24 2,15 5,1625 2 (5,1625 2,1875)25 16 5 4 25 100 100 5

    + + = + + =

    316 24 215 2975 2 35 215

    100 100 1000 5 10 100+

    = + =

    5,810008500

    100011907310

    5100025595

    ==

    +=

    + .

    2) =+=++108

    165

    725

    10003648,0

    212125,0:

    165

    257:364,0

    8,51058

    1020

    1025

    1013

    522425

    1258212585

    7254025527

    ==++=

    +

    +

    = .

    6. 1) 16, 9 .2) 7, 25(4) -

    .3) 1,21221222 ( n )

    .4) 99,1357911( )

    .7. = ...5677643,531 57,5 . 5, 4 5, 5

    31 , 5, 5 5, 6 .

    8. 1) 75x = ; ...6457513,27 , , 57 < . ,075 > , , |x|=x.

    2) 534x = . 4 53 , -

    : 1642 = ; 45)53( 2 = . , 45 > 16, -

    , ,453 > , , 0534 , 105 > , 0105 > , , , xx = .

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  • 89. 1) =+=+ )322()322)(322)(324()223)(38(

    1983)22()322( 22 ===+ .

    2) === 2)332()332)(332()332)(227(

    31312)312274( =+= .

    3) 2)2425(2)2425(2)2450( 2 +=+=+ 18229 == .

    4) 3:)3335(3:)3335(3:)2735( 2 +=+=+ 83:38 == .

    5) 832133213)13()13( 22 =++++=++ .

    6) 5615541205215)152()15( 22 =+=+ - .

    10. 1) 4272372372863 22 === ;

    2) 10552552520 2 === ;

    3) 5,22:522:258:50 22 === ;

    4) 323:233:2327:12 22 === .

    11. 1) 89,3 + 171,1 + .

    2,3129,112,31289,3)89,3( 2 +=++=+ ;

    7,182287,1821711)171,1( 2 +=++=+ .

    )2,31228()7,18228( ++ ,

    , 89,3171,1 +>+ ,

    , 89,3171,1 ++ 7,18228 2,3129,11 + , -

    : ;2,3127,1829,1128 >+ ;2,3127,1821,16 >+

    ;8,1247,184,648,7421,259 >++ 07,184,6421,209 >+ -

    , 89,3171,1 +>+ .

    2) 1,211 1,310 .

    , 1,211 > 1,310 ;

    3121,3101,2321,211 +>+ ; 3121,232 > ;

    3121,232 < ; 311,23 < , , -

    1,211 > 1,310 .

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  • 912. 1) ( 7 2 10 2 ) 2 5 (2 35 10 10 2 10) + = + =

    7 3 7 3( 2) 2 5 ( 5 2 5) 102 2+

    = + = = .

    2) 16 2 16 2( 16 6 7 7) 3 ( 7) 32 2+

    + = + 333 == .

    3) ( 8 2 15 8 2 15 ) 2 7+ + =

    = 8 64 60 8 64 60 8 64 60 8 64 60( ) 2 72 2 2 2

    + + + + + =

    8 4 8 22 2 7 2 2 72 2

    = + = + = 322

    172

    17734 +=++=+ .

    13. 1) n2n 5b = , : 2

    1 5b = , 4

    2 5b = , 6

    3 5b = .

    , 2555

    bb

    2555

    bb

    q4

    6

    2

    32

    4

    1

    2====== , , -

    .2) n3n 2b = ,

    31 2b = ,

    62 2b = ,

    93 2b = .

    , 6

    9

    2

    33

    6

    1

    2

    22

    bb8

    22

    bbq ===== , , -

    .14. 1) ,88b4 = ;2q = ;qbb

    314 = ;8b88 1 = .11b1 =

    341113121

    )321(11q1

    )q1(bS

    51

    5 ==

    =

    = .

    2) ,11b1 = ;88b4 = 3

    14 qbb = ;3q1188 = ; ;8q3 = .2q =

    341113121

    )21(11S

    5

    5 ==

    = .

    15. 1) 1, ,51 ,

    251 , ,

    251b3 = 5

    1b2 = ; ,51:

    251

    bb

    q2

    3== 1q < , -

    , .

    2) 31 , ,

    91 ,

    271 , ,

    271b3 = 9

    1b2 = ;

    31

    91:

    271

    bb

    q2

    3=== , 1q < , ,

    .

    3) 27, 9, 3 , ,3b3 = 9b2 = ; 31

    93

    bb

    q2

    3=== , 1q < , ,

    .

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  • 10

    4) 64, 32, 16 , ,16b3 = 32b 2 = ; 21

    3216

    bbq

    2

    3=== , 1q < ,

    , .

    16. 1) 40b1 = , 20b 2 = ; 21

    4020

    bb

    q1

    2=

    == , 1q < ,

    .2) 12b7 = , 4

    3b11 = ; 10

    111 qbb = ; 6

    17 qbb = , ,

    ,16112:

    43q

    qb

    qbbb 4

    61

    101

    7

    11===

    = , ,121

  • 11

    18. 1) 1q ,2

    = 11b8

    = ( )181

    12

    b 1 2 1S1 q 8 3 121

    = = = =

    .

    2) 1q ,3

    = 51b81

    = ; 45 5b b q= ; 11 1b81 34

    = ; 11 1b81 81

    = , ,

    1b 1= ; 1 1 23 3

    b 1 1S 1,51 q 1

    = = = =

    .

    3) 1q ,3

    = 1b 9= ; ( )1 41 33b 9 9 27S 6,75

    1 q 41= = = = =

    .

    4) 1q ,2

    = 41b8

    = ; 34 1b b q= ; 3

    11 1b8 2

    = , 1b 1= ,

    , ( ) 31 221 1 2S

    31

    = = =

    .

    19. 1) 6, 1, 16

    1b 6,= 2b 1= ; 21

    b 1qb 6

    = = ; 1 1 56 6

    b 6 6 36S 7,21 q 51

    = = = = =

    .

    2) 25 , 5 , 1 , 1b 25,= 2b 5= ; 21

    b 1qb 5

    = = ;

    11 45 5

    b 25 25 125S 31,251 q 41

    = = = = =

    .

    20. 1) 0,(5). :

    1055,0a1 == , 22 10

    510555,0a +== , ,...

    105

    105

    105555,0a 323 ++==

    , :

    +++=32 10

    510

    5105a

    510

    110

    5a S91

    = = =

    .

    2) 0,(8). :

    1088,0a1 == , 22 10

    810888,0a +== ,

    , :

    2 38 8 8a

    10 10 10= + + +

    810

    110

    8a S91

    = = =

    .

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  • 12

    3) 0,(32). :

    1003232,0a1 == , 22

    32 32a 0,3232100 100

    = = + ,

    , :

    ...100

    32100

    3210032a

    32+++=

    9932

    1Sa

    1001

    10032

    =

    == .

    4) 0,2(5). :

    100505,0a1 == , 32

    5 5a 0,055100 100

    = = + ,

    , 0,2:

    9023

    90518

    905

    51

    151S2,0a

    101

    1005

    =

    +=+=

    +=+= .

    21. 1) nn )2(3b = ; 6b1 = ; 12b 2 = ; 24b3 = ;

    1224

    bb

    26

    12bb

    q2

    3

    1

    2 ===

    == , 12q >= , -

    .2) nn 45b = ; 20b1 = ; 80b 2 = ; 320b3 = ;

    80320

    bb4

    2080

    bbq

    2

    3

    1

    2

    ===== , 14q >= , -

    .

    3) 1n

    n 318b

    = ; 8b1 = ; 3

    8b2 = ; 98b3 = ;

    3898

    2

    338

    1

    2bb

    31

    8bbq

    ===== , 131q

  • 13

    : 2b1 = , 1 12

    b 2S 2 21 q 1

    = = =

    .

    2) 23q = ;

    89b4 = ;

    314 qbb = ; 8

    33b89

    1 = ,

    : 3b1 = , 13

    2

    b 3S 2 3(2 3)1 q 1

    = = = +

    .

    23. 1) 30S = , 51q = . ,

    q1b

    S 1

    = , , .24)511(30)q1(Sb1 ===

    2) 30S = , 20b1 = . , q1

    bS 1

    = , , Sbq1 1= ,

    31

    321

    Sb1q 1 === .

    24. 1) n

    n nn n