# ГДЗ - алгебра - 10 класс -Алимов - 2001

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- 10 - - 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