matematika 8 - zbirka (krug)
DESCRIPTION
Matematika 8 - Zbirka (Krug)TRANSCRIPT
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650-02-00299/2010-06 21. 07. 2010. , .
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37.016:51 (075.2) (076)
, , 1938- 8 :
8. / , ; [ , ]. - 6. . - : ,2011 ( : ). - 157 . : . , ; 24
10.000.
18 978-86-7136-193-4 1. , , 1954- []
138.8- 183736588
18 978-86-7136-193-4 : 10 000
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8. , 2009. . , 8. , . :
1. ,2. , ,3. ,4. ,5. ,6. ,7. ,8. ,9. ,
10. ,11. .
, - . . , .
, - .
, 2010.
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7
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X X
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1. .................................................................. ,1.1. .............................. .................................... 1.2. ................................................................. 41.3. ....................................... 61.4. I .......................................................... ................. 7
2. , .................................................................. 92.1. , - ....................................... 92.2. .................................................................... 132.3. I I .............................. ............................................. 14
3. -............................................................................................ 16
3.1. ........................ 173.2. ........................ 233.3. .................... 273.4. II I ........................................ 31
4. .................................................................................................. 364.1. .......................................................... 374.2. IV ........................................................................... 44
5. ............................................................................................ 455.1. ..................................................... 405.2. V ........................................................................... 52
6. ...................................................................... 556.1. = + ........................................................................... 556.2. - .............................................. 026.3. V I........................................................................... 55
7. 67
I
-
8. . 718.1. ........ 728.2. -
.................................................................................. 788.3. V I I I ........................................................................ 84
9. ..................................................................................................... 879.1. ............................................................ 879.2. IX ........................................................................... 90
10. ...................................................................................................... 9310.1. .......................................................... 9310.2. X ........................................................................... 96
11. ........ ......................................................................................... 9911.1. ......................................................... 9911.2. XI......................................................................... 100
12. .............................................................................................. 1031. ............................................................................. 1032. , ........................................................................... 1093. ..................... 1124. ................................................................................................... 1215. .............................................................................................. 1256. .............................................................................. 1307. ........ ..................... 1388. ................................ 1409. .................................................................................................... 14610. ...................................................................................................... 14911. .................................................................................................... 153
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1.
- .
1
1.1.
. , - :
_ ~ ~
1 _
^~~'
1. , , 6 . , . : 6 = : , :
) = 3 , 6 = 4 , = 5 ;) = 7 , 6 = 5 , = 6 ;
) = 8 , 6 = 3 , = 5 .
1 1 (1769-1821),
-
2
\(; 2 , 6, 1.
:/ 2( ) : 6 = : ; ) = ;
) X = + 6
) = -; ) =
6
& &
3. :) ; ) ;
.
/I 4.1 :^ ( ) 2 : 3 ; 6 ) 1 : 4 ;
... ) 2 : 3 : 4 ; ) 2 : 5 : 3 .
( (' . :
) ; )
) 3 :5 ;
( ) = /.\ :5
) = - 1 ; ' 3
) = - ;' 8
) = 1 - . 5
6 . () [| > :
) ^ , = , = ;) 8 = 7 , 8 = 2 8 , = 1 4 ;) = , = 4 , 8 = 9 .
. . 67. > . = 10 , = 2 = 15 , .
8 . (). - :
) = 12 , = 4 , = 8 ;) = 15 , = 3 , = 25 .
9. ) (> 6 , ) . :
) > = 8 , = 20 , = 6 ;) > = 2 0 , = , = 4 .
-
1. 3
. . 8 . . 10
10. / ' ' ():
) = 12 , = , ' = 8 , ' = ;
) = 14 , = , ' = 7 , ' = ;
) = , = 15 , ' = 9 , ' ' = 8 ?
11. . .
0 1,5
12. || .
) = 7 , = 2 1 = 1 0 , .
) = , = = 10 , .
) = 7 , 1V = 2 = 14 , .
) = 2 5 , / = = 4 , 1 .
-
4
1.2.
1 1 1 , - :
\ , /3 = /? 7 = 7 , : 6 : = : : 1
: 1 11 ( ~ ^ 1!) :(1) (. = , /3 = /^);(2) - , - (. : = 6 : , 7 = 7^);(3) - (. : = : 61 = : \ );(4) - (. : 61 = : \ , 7 = 71, > 6).
/ = = = .1 &1 1
13. :) 4 , 5 , 8 , 10 , 12 ;) , 4 , 9 , 1 5 , 1 8 ?
14. 4 , 3,6 1,6 . 1,6 ( = 1,6 ).
15.. = 20, = 16. &1 = 21, = 11,2 . 6 .
-
1. 5
16. / = 30 = 45 '^ ,
. .
17. = 18 = 12 32 , , . - .
18. = 15 , 6 = 12 = 8 . - .
19. = 25 = 12 , = 8 . .
20. = 18 , 6 = 16 , = 9 . .
21 . , :
1 ;
2 ;
3 - .
22. = 30 , = 24 , = 20 . 1 .
23. = 12 , = 15 , = 18 5! = 60 .
24. = 4, 6 = 6 = 8 .
= .
25. 2 : 5 : 6 . \ = . .
26. I .
) 1
-
6
) I ?
) I 1
27. 8 . = 9 , = 4 , 8 = = 2 , 8.
28. = 7 , 6 = 15 = 12 . 26 . ?
29. = \ / 5 . .
30. . .
31. 8 . = 12 , 8 = 4 = 9 , .
32. - 12 : 5. 60 , .
1.3.
, , = = = , , > . :
= - , 2 = , 2 = .
-
1. 7
33. :) = 3 , 6 = 4 ; ) = 5 , 6 = 1 2 ;
, .
34. 6 , , , =
-
41. = 12 6 = 4 . 0 , [). .
42. = 8 = 4 , = . .
43. ( = ) . . = 12 = 8 , .
44. = 12 , 36 2 , . .
45. . 5 52 , >. = 2 , = = , .
46. . 1 . , 1 , = 4 = 9 , .
47. .
= 1.
48. = 12 6 = 4 . .
49. I) = 7 , .0(7 = 9 = . : .
50. , .
-
2. ,
, 1 ( - )
()
, . . . . . . , 1 .__________________________________
2.1. , -
51. . :
) 3; ) 4; ) 5; ) 8; ) ?
52. , . : ) ; ) ; ) , ?
53. , . ?
-
10
54. :
) 36; ) 66; ) 105 ?
55. , , , >, ?
\ *
*
. . 55 . . 61
56. . : ) ; ) ?
57. , , ?
58. :) 15; ) 20; ) 30
?
59. :
) 56; ) 120; ) 20 ?
60. 10 . ?
61. , 6 ( || 6) , , (). ?
62. , , . : ) ; ) ; ) , ; ) , , 0 4
63. . 5 ? .
64. , , 5 , 5 , , 5 . ?
-
2. , 11
65. ?)
.)
.) .) ?
66 . . ) ; )
?
67. . ) ; )
?
68 . . ?
69. . , ?
70. . ?
71. . ?
72. () :
) ; ) .
. . 72 . . 73
-
12
73. ^ ^ . .! ().
) ?
) ?
) ( )?
74. ) . ?
) . ?
75. : ) ; ) ; ) /?.
76. ?
) , _ .
) , 7 || 7 /3 _1 7 , 1 (3.
) (3 , 7 /3.
77. ^^ ^ (). :) ;) ;) ;) ;) , /3 7 1 /3
(3 7 , || 7 ;)
.
. ?
) , .
) , .
) , .
) 0 , /3 7 || 0 /3 || 7 , || 7 .
1
. . 77
-
2. , 13
2.2.
79. :) ; ) ; )\; ) ?\ ) ;
)80. N .
/ :/- ) ; ) ? / / ?
! 81 : > "-- %' 4-7 ;) ' ' = 8 , ' = 24 , ' = 18 ; --------
) ' ' = 12 , ' = 10 , ' = 5 , ' ' 7, .
, 82. . ' ' :
| = 15 , ' = 4 , ' = 8 ;) = 6 , ' = 1 , ' = 2 .
83. = 40 ' = 45 ' = 21 . : ) 0~~'( ) ' ;
) , ;) ' . ' 2-;
, \
84. , - 4 ' 7.
7 7:/
/ ) 30 ; ; / - 6 )4 5 ; )6 0 . *
, 8 . 12 : 2.. , -..
( ; ( - ' '' ' " ~ "1' ' ^) ?
8^. . = \ /
' ' = 1,5 ; ) ' ' = , 2 ' ' , ,^ , . ( \ \
-
14
\ 30, 45, 60. .
8 = 15 & = 20 45 . .
89. , :
\) 5 9 ; ) 7,4 2,6 .
, 90* . :
) ' ' = , ' = 1 , ' = ;) ' ' = 5 , ' = 4 , ' = 8 ;) !' = ' = 8 , ' = 7
! '
\ \ :
) \ . . . ;) . . . ; ^) . . . ; /) . . . ;) . . . ; } ' ) . . . . '
[ .
(). :
. . 91
2.3. II
92. :) ;
) ?
93. 12 16 3 = 8 = = = 26 . 8 .
94. . .
-
2. , 15
95. . 3 5 . 5 ?
96. , , . ,
-
3.
1 / 1 ( )
()
= 6,
6 .
1 0 3
= - .
2 = 0, 6 0
, 0 0 = 6 . .
3 = 0, 6 = 0
, 0 0 0 = 0. .
< 6, ^ 6, ^ 6, > 6,
6 .
-
3. 17
3.1.
103. :. :
> 2 = 2; )X = 5 ; )
23
1~~ 2 )
7~2 ~~ ~~ 3 _ _ 5 2 6
2
7 = '
107. ( ):) 2 + 1 = 2 ; ) 0 -2 = 1 ; ) 2 + 2 = 2 + 2 ;
) /2 = 2 ; ) 2 - 2 = 2 2 - 7 ; ) - = 1?2
108. : 3 2
) 2 ~ 4 = 5 ; . )24
) 22 = 16; )22 _
:
) 2 2 = 2 ; )7
II(1 )32 ~2 ~
2
4
. .
^ I
-
18
110. :) 5 2( + 5) = 20 = 5;) 2 + 1 = ( + I )2 = 0
, ) 6 = 2 = 1
.
111. :1 1
) 2 = 0 + 2
= 2 + 2
. ( I )2) ^ = 0 - 1 = 0 ;
1) ( 1)( 4) = 1 1?
112. 2 5 = 13 2 6 = 21. , ( )? .
113. (. ):) 0 = 0 ; ) ( - I )2 = 2 - 2 + 1 ;
) ( + - 1
) 5 + 2 = 7;
9 ) 2( - 3 ) = 3;
5 ) ^ = 7 .
114. 0 :) 1 = 2 1 ;
) 1 = ;
115. :
);1 = 12;116. :
. 3 7 138.) -- --- ---
} 10 1 0
) 2 = 0 ;
) [ 1| + | + 1| = 2 .
) 4 = = /8-,V 2
) %/: 12.
I1 ; 1 -117. 3:
) - 1 )2 5
= 1 .
4 5
-
3/
) - 1 = 2 + 3;
?
1 _ 1 3 3 + 2 '
( 118-127):
118.)) 3 = (2 - ) = 6 - {2 + 1); ) 9 - (8 - ) = 7 - ( - 6)) - (15 + 2 - (5 + 11)) = 2 - 8 ;
) 8(2 - ( + 2)) + 18 = 7 - ( - 5(2 - 4));
) - (4 - 5) - 28 = 2 - (5 + ( - (2 - 3))).
119. ) 26 - (20 - (10 - ) - 7) = 30 - ( + 7); ) 2 - 3(2 - 3(2 - 3(2 - 3))) = 1 ;
) - (2 - ( - (4 5))) = 1.
( 120. ) (4 - 3)(3 + 4) - (2 + 1)(6 - 1) = 1;
@1 ( - 10) ( - 1) - ( + 1)(3* - 4 ) = 2;() (3 - 5)2 + (1 + 12)2 = (13 - 2)2 + 6 ;
' 2( - 1)( + 3) + ( 7) = (5 + ) + 10;) ,(2 )(3 ) (1 )(5 ) -= 0.
121. ) ( - 2 ) : 2 = (2 - 1) : 3;
) ( + 1) : ( + 3) = ( 3) : ( 2) ;
) (7 + 3) : (7 - 4) = 5( + 1) : (5 ~ 2);) : ( + 1) = (2 + 1) : (2 - 1).
122. ) ( + 3) : (1 ) = - 2 ;
) ( + 7) : (13 - ) = (5 - ) : (5 + ) ; + 7 3
2 ) 0,35 : 0,7 = ;
3 'I ' ' X
) (2 + 1) : ( + 2) = (6 + 5) : (9 + 8).
) + 2 1
3 - 2 ~ ~ 2
. 2 + 12123. ) = 2 ,5 ;
+ 3, 2 - 3 ..
) - 7 6
2 + 5 ~ ~ 7
) 1
-4. + 1 2
-
20
124, ) -2 - 5
= 4;
-*
.)
+ 2 - ^ - 1 .5 2
2 3 ?+ 1 - 11/ 5 10
5 2 3
, 2 I 1> ^ - = 1 2 ;
0 . / ^ ^ > + ^ 1 , 1 2 . 2 3
125. + 2 - 1 4 - : (--- : - ~ >1
)
6 + 1
;( ) 4 ( X + - | - -
2 2( + 3) ^ >
. 2 1> * + 3 1 3
+ ?
\ 5 24 7) 6 " 8 (^ 4) = 5 ;
1 , 1 10 3 _ 2 ~ 4 + 2
. 2 + 3 5 - 14 + 1) - ------------
1 + 1 1 1 + 126. ) ---------- --------------------+ 2 = 0,
)
127. ) - -
4 + 2( + 1) _ ^ = 5( - 3) + 2 _ + 433 ' 4 2
4 + 4 - 1 _ 5 + 1 3 4 _ 7
- ~ X - - ) - 1)
+ 7 / + 1 5 + 7 / + 1 - 1 \8 V 2 16 V 4 8
7 7 , 1-4--- ---------- 1-4 --- 61 + 4 2 1 + 5 2
) - +
1
2 ' 66
) - + X -
24 3 + 2 3
12
= 3.2 ' " 3
128. = 0 = 0, :
) ( 1)( + 1) = 0; ) 2( 3)( + 1) = 0;) ( - 1)( + 2) = 0; ) 4 (3 + 1)( - 3) = 0;) ( 2)( 1)( + 1) = 0; ) 5( + 1)( 2)( 3)
+ 1 2
= 0
= 0.
-
3. 21
129. = 0 = 0 / 0 , :
. - 1) ----- - = 0 ;
' + 1 2
) ( + 1)( + 2)
) < ^ = 0 :
= 0 ;
= + 1> ^ = ; ( + 1)( - 2)
1 = 0 ;
^ ( + 2)( 3)( + 5) = ^( + 2)5 + 1
( 130-133):
130. ) (2 - I)2 - ( + I)2 = 0; ) ( - 5)2 - (2 + I)2 = 0;) ( + 5)2 - ( - I )2 = 48; ) ( - I )2 - ( + I )2 = 2,5 - ;) ( + I)2 1 = 2 + 2 ; ) (2 + I )2 = 2 (2 - 1) + 6;) (2 )2 ( + 2)2 + 26/ = 1.
2131. )
)
0 1 - 0 -
( 1)( + 1) (2 + I )2 1---------,------------------ "---- = 1- ;
12
) 1 2
1 ;
132.
2 ) \ 2) ( + 8)2 + ( + )2 = ( + 12)2 + ( - 5)2
, ( I )2 ( 3)(2 5)2 4
(6 2)( 1) 6
= 3 ( 2);
= 4:) ( )2
) ( + I )2 + ( + 2)2 + ( + )2 + ( + 4)2 = (2 + 5)2 .
133. ) 1 - -; 2 + 2 ( - - 3 \ ( 2 - 1 )
4
) ( - I )2 + ^4 - 0 = ^5 + ^
) ( - 4)2 - ( + )2 = 3( - 9);
) ( + +2) ( + +3) ( + - 3 = 1.
-
22
134. ) ( 3) + ( + 1)(3 ) 7 - 5 - 2 ----------- - = 3.
)
3 2
+ 2 2 4,5 ( 2)2 = 2 +
- 17.) 7 = + 10 + 11 = 6
.4
) 4 + - = 0
(. + I )2 5 = ( + 3)( + 1)
135. ) (2 )(3 ) = (5 + )( + ) 1 ( )2 ( + I )2 = 2( 6).
) (5 + )( + ) = (2 )(3 ) + 1 2 1 + 1 + 4
--------9
= 1 -12
136. :2 5 5
= - \-V = 1. 2 3 2
) , .) = .
137. = ( 3, 2, 1,0,1 , 2,3} -:
) + \\ = 0 ; ) 1 + \ 1| = 0 ;) \ 1| + | + 1| = 0 ; ) | 1| = \ + 1)?
( 138-141):
138. ) \2 3| + 1 = 4; ) 2\ - 3| + 4 = 8 ; ) || + 7 = 13 - 2\\;) 3 = 2\; ) \2 7\ + = 5; ) \ + 2| = 2 + 1;
) - | + 1| = 2 ; ) |3 2| + = 11.
139. ) \ 1| + | + 1| = 2; ) [ - 2| + | - 3| + |2 - 8| = 9.
140. ) 2\/2 4 + 4 = ; ) / 9 6 + 2 + 8 = 2;,_____________ 7
) /92 6 + 1 + = 15.
141. /.2 4 + 4 \/42 + 12 + 9 = 1 .
-
3. 23
3.2.
142. 866. ?
143. 99. ?
144. 167. ?
145. 5 . ?
146. , 1 . ?
147. 12 . ?
2148. - , 23
0. , ?
149. 22 . ?
3150. 112 .
, ?
151. 28 , 4 . ?
152. 30 , 10 . ?
153. 36 , 16 . ?
154. 2 2?
155. 4 : 5 . 12 , .
156. - 2 7
- ?3
-
24
157.
?
158. - , 33. ?
159. 6, 9 7, 13, 19. .
160. 38 .
161. 9, 3. .
3162. - .
, . .
163. , - , , . ?
164. 18 - , 5 . , , . ?
165. 6
.
20%. , 5 6 . ?
2 2166. 4 , -
5 5. ?
167. ; , 720 . ?
-
3. 25
168. 12 48 / . 45 80 / . ?
169. 2040 87 . 23 232 3 . ?
170. - . 60 , 40 . 100 . 20 ?
171. . 1 10 , 1 12 . 36 , 1
172. 1 ,
. .
173. 2, 5, 11 1, . ?
174. 4. 9, . .
175. 4. , 16 . ?
176. 7 8 , 378 25 8. ?
177. 30 , 25 . ?
178. 150 12%- 4%- ?
179. 80%- 121 60%- . ?
-
2
180. 60% 90% 101 80%. ?
181. 5 . 3 , 1 , . .182. 5 , 1 . ?
183. 8 6 , 4 . ?184. 8 . 2 . ?185. . 2 , 4 , 2 . .
186. 2 , 20 3 . ?187. 14 . 1 , .188. 1,5 2,1 32 1,65 . ?189. 10 21 48 33 ?190. 1,50 . , , . ?191. , , , 10 , 12 , , , 4 . ?192. 4 . 24 ?
-
3. 27
193. 7 . 4 , 28 ?
194. 60 . 4 0 / , 5 0 / . , . ?
195. , , , , 40 . 4 / 45 . ?
196. ; 2 48 , 4 40 . 2 6 / . .
3.3.
197. :
198. :) 2 > 2 3; ) 25 < 52;) 43 < 3 4 ; ) 7 62 ^ 8 72 ?
199. X = { 3, 2, 1 ,0,1 ,2 ,3 ,4} - :
) 5 1 < 3; ) ~ + 2 < - 3 ; ) 1 - 2 > 3;
/ ) 3 - < 1 ; ) | |< 2 ; ) || > 3?
200. : ) + 1 > 2 ; ) 2 ?
-
28
201. :. 4 1 5 2 1
----------- 2 < ^5 6) ^ 1 - 2 ( 1 + 3) < 1 .
202. - (. , > , < < , ):
. 3< - 1 ; ) 2 - 5 - ( + 2) < - 5 ;
) 1 - ^ 2 ;
) - 2 < 8( + 1);
. 2) 3 ------- < 1 ;
) - - 2 ( + 1) < 0 ;
) 2 ( ^ 2 - - - 3 < 0 ;
. 2 1 )
203. - :
. 2 3 . 1 ) 4 - > '
204. :
) + 5 < = 2; ) ( + I)2 < ( - 3);
) (2 ) ^ 3( I)2 ; ) - > 0.
205. :
) + 9 > 4 3; ) ^ - 1 < 0,1 + - ;4 2
2) - 1 < 0,2 + 2.
206. 5 - 10 + 15.
_2 ) |207. -------- --------
3 2 1.
208. :
) - + 5 > 0; ) 4 - 1 < 15; ) - + 2 < 0; ) - < 5+1.
-
3.
( 209-214):
209. ) 5 - 3 < 4 1;
) 6 - 2 < 12 + 19;
) 6 < 8 2 2 - - .2
- 3 4 ) . X ~ 3 1 - 1 ;
7 + 17
1 + 7 . - + 6, 4 1 + 5 2 1 2 ) -----------------------------------< -----------------
2 24 12 3 6 ^ __ 20 - (10 - ) 26 - 51 2(1 - ) ) X ----- + . ---------------------- ------------------------
156 ^ 52 13
214. ) ( + 4)( - 3) + 10 < ( + 2)( + 3);) ( + 3)(2 - 1) - (2 + 1)( - 4) > 0;) ( - I )2 + 7 > ( + 4)2;) ( + 1)( + 2) + 3(1 - ) < ( - I ) 2 .
-
30
215.
2 + 1 1 -----------------2 ~ > '
216.
2 40,5(2 - 5) > ------1, 0,2(3 - 2) + 3 > - 0,5( - 1).
2
:) < - 2 , < 1, -2 ,5 < ^ 2;) 1 < < :2, 1,5 < ^ 3 , * ^ 2,7;) + 7, > 3, 5 ^ < 11 1
) X +1
~ 2 2 < < 0 , -1 < < 3
) X > 2, > 14,
\
218. :) 5 > 0, < 17; )2 1 0, 4 < 0 ;
) 1 , 1 7 52 (1 - 4) > * ,
5 47 13 11 + _ 2 1 ^ 3 ~ 2 1
. 5 4 3 , . . . ) 3 - > ------- ----------- ----------- , 2(2 - 5) 27 (2 + I )2 ;
+ 1 + 2 + 1 + 2 2 3 6 2 3
) 15 - > 2( + 1), 4( 4) ^ 14.0
219. :1 14
) 15 2 > 2 2( 4) < ------- ;3 2
) 2(3 - 4) - 16 < 3(4 - 3) 3( + 1) < 2 + 4; 6
2 13 2 , 20 ) > 2 - - ( - 7) - ---------- - + < 2 - 1 - ^ + ^ < 3 1 - 2 3 2 8 2
-
3. 31
( 220-222):
220. ) | ^ 2; ) || > 3 .
221. ) \ - 2| < 1; ) \2 1 1; < 1; ) 3 > 5;) \5 - 1| 5= 4; ) |3 2,5| ^ 2; ) |5 2\ < 1.
222. ) 2 + ( 1| > 5; ) \+ 1| - ^ < 1; ) \2 - 6| ^ 9 ;
) 1 > \2 4 |; ) |2 - 4| < 2 - .
2 ~ / 100223. = - < 18? 3
224. 2 5 3 17?
225. (2 + 1)( 2) 2( + I )2 , , ?
226. . 9 1100 , 1200 , 13 1500 , 1600 . ?
3.4. III
227. :
= { | < < 3 }, = { | < ^ 3 } = { | 3 < < + }, = { | 3 < < + } = { | I ^ < 4 }, = ( I ~1 0X
< 0 4
X X
II
/ '
\
\
. 6.1 . 6.2 . 6.3
+ = 0, . = / ( 0) - . /() = \ + \ / ) = ^+ 2 -------- ;------ \ = % . = - -, . 6.4.
. 6.4
-
56
6.1. +
451. :
) = ; 6 ) / = / ; ) = ---------- ;
) = 2 - 2 + 1; ) = / + 5;
) = ( - I )2 - 2; ) = - ?X452. :
) = + 1; ) = -~ 2; ) = _ + . : 1, 0, 1, 2, 3 .
453. = /() :) 2 + - 5 = 0; ) - 7 + 4 = 0; ) 6 + 9 = 0.
: 2, 0, ,
.
5- -
454. = / () '() = 2 3. : ) / ( 0 ) ; ) /(1 ) ; ) / ( - 1 ) ; ) / ( + 1); ) / ( 2 - 1 ) ; ) / ( / ( - 2 ) ) ; ) / ( / ( * ) ) .
4455. /( ) = + 1, :
5
) / ( 0 ) ; ) / ( 1); ) / ( | ) ; ) / ^ - 1^ .
456. :) = 1; ) = 2 7\ ) = 4 - 4;) 2 + 3 = 0; ) 15 17 + 30 = 0.
457. :) V = 1; ) = - 2 ; ) = 0; ) = 3; ) = 1; ) = 0.
458. :) = X, = 1, = + 1; ) = - , = - - 1 , = - + 1 ;
. 1 1) 2 ~ ^ ==2 '^ " 1 ) = 2, = -2 + 1.
-
57
459. : ) 2 2 + 4 = 0; ) 4 = 0;
) 14 + 7 21 = 0; ) ^ - ^ / + 1 = 0.
) 5 - 2 / - 3 = 0 ;
, .
460. :
461. :) 8 2 + 4 = 0; ) - 6 + = -1 2 ; ) 0,6 + 8 = - 3 - 2.
+ 2. ? .
463. + 2 4 = 0.
) .
) .) .
464. = 2 + 1
) = 5 + 6;
462.
1) + / 2 = 0;3) - - 2 = 0;
2) + 2 0;
4) 2 + 3 = 0
()?
) )'
X
. . 464
/
-
58
465.
)
)
466.
)
)
467 .
. ()?
)
. . 466
*) = ; ) = ; )') = - 2; ) = - - 2 ; )
: = + 2 ;^ = + 2?
6. 59
2 1 X
+ 2 -1-1
. . 167
468. :
) = + 2; ) = -
?
V
V
/ 2 \
/ \\ 2 ^
. . 468
-- 2; ) = ~
\ \ .
,469. ( 1 1) ( 2 , 2) (2,0)? 1
470. 6 = + 6 :) 0 (0 ,0 ) ( - 1,2); ) 0 (0 ,0 ) (3 ,6 ).
471. = (& - 3) + ; : (3 ,-1 ) . . I !\9
472. - 6 = 12 -.
473. :
) 2> 2 = 12; ) 2 + 5/ + 10 = 0.
474. :
) (0 ,-3 ) , 5 (1 ,0 ); ) /1(0,- 2), 5 (3 ,0 );) -4(0, 1), 5 ( 1, 2).
475. :
) = 2 1] ) = 2: + 1; ) = - 2 + 1;
) = - 2 - 1 - ) = ^ + | ,
4 (1 ,-1 ) 5 ( - 1 ,3 ) . ?
-
60
476. - :
) = - \) = - + 1;) 1;) + 1;) = - 1 ?
477. (3,0), { 7,5)
/ = - - 2 1
478. ) : = + 14, (2 ,4); ) - = + , {3,4);
/ 14 \ ( 4, I
: ) : = + 3, (5 ,2 );) : 2 + = 0, { - 1,1).
479. = ---- -1 5 2 -, = .
480. = + 5 :
) -; ) = + 3.
481. = { 1) { + 1) = 2 + 5. .
482. :
) : = + 3, { 1,2); ) : = - 2 + 5, (-1 ,3 ) ;
) - = ^ + 1, {4,2).
483. = + 4. = 2 .
484. : ) = - + 4; ) = 2 + 2; ) = - - 5 ;) = 5 = 7; ) - + 11 = 0; ) 2 + 2 + 3 = 0;) = 0; ) 4 + 1 = 0 ?
-
6. 61
485. :
) /= (2 4): 3; ) = (7 + 5) + ;) = ( - 11); + 2 + 3; ) (5 - ): - 2 + 4 = 0;) (2 - 7) + 1 = 0.
486. , :
. 2 1 _ ) = ~ + ; ) = + - + ?
I487. :
) = 2 - 4 ; ) = - + - ;5
) = ~ + 1; ) 2 ,3
.
488. :
) - 2 = 0, + = 3, : + 2 = 8;) + = 3, = 1, 2 = 6. '
489. :
) = \ ) = ( - 1) + 2 - 1;
) = - + 1; ) 2 - + + 1 = 0;
) ( - 2) - (1_ ) + \ + 1=' - .
490. + 3 ( 2, 5). (1,2) ( 7,6)?
491. = 2 + 4 . .
-
62
492. = + 2 . 1 .
493. (0,6) 9.
6.2. -
494. ( 1, 2) 2 = . .
495. = ( 8) + 4. = 2 .
496. :
-.
) 2 + 1; ) = + ^ ;
) + 2 + 6 = 0; ) 4 + 5 1 = 0.
497. = (26 1)+ ( 6
- 8.
498. ( ) :
.
499. :) = 6;
< 0, ) 2 4 + 8 = 0.
0, > 0.
500. :
.
-
6. 63
501. :) = 2 + 5 ; ) = 2 - 3;
) = - + 8; + 3 = 0.
?
502.
( - 2)* ( 1), / .
: - :
.
504. - - :
505. - - = 2 1 + 2.
506. (4 - 6) - (3 2). :
) = 2;) = 10 + 1;) { 3,2) .
507. ) ?) 3 + = 12
6.
508. = {) : /(1 ) = 2, /(0 ) = 1. /() = + .
509. = + {2, -1 ) { 3,1) .
510. = 1 .
) = 2 - 6; ) = - + 8; ) 5 - 5 + 10 = 0.
503.
-
64
. . 511
511. ( ) = + .
512. 5 + 2 = 9. :
) (1, ) ; ) ( ,3); ) (1 /5 ,0).
513. 6 + = 1 2 = 6 + = 0.
514. (1,3) = ( 1) 4 + 1 .
515. () = 2 + 1.
= / . = / , = /(2 ), 2/ = / ( / ( ) ) .
516. = + ^ + 1 2.
) ( 4,6) .
) .
517. ( ) = 1. : ) / ( ) = 2; ) / ( ) = 3; ) / ( ) = 0; ) ! ( ) = /(2 + 1); ) / ( / ( ) ) = 5; ) / ( ) = .
5518. = ( 1) + - , 6 .
- 2. .
-
6. , 65
519. / (), = / ( )
) / ( - 1) = 2 - 3; ) / ( 2 - 1 ) = ;
520. :) = ; ) = \\ + 1;) = 3 - \\ ; ) = - \\ ;
) = ) = +
) \ + 2) = + 1 .
) = \ - 1|; ) = + \\;
6.3. V I
521. + 1 = 0, + - 8 = 0 - 2 - 2 = 0 ( I ).
522. = - 4 2 + 2 = 0 ( IV ).
523. -
= - 2 + 2 = - - + 3 ( ).
524. = + 1 = + 2 .
525. ( 3, 4) - 14.
526. :) + \\ = + \\ ; ) - || = - \\; ) - \\ = + | |;) \\ + 3 = \ + 3 |; ) \\ 2 = \ - 2\ .
527. :
) \ + \ = 1 ; ) ^ + = 2-
) + \\ + + || = 16; ) || + |/| = 1;) | - 2 / | < 2 ; ) + | < 1 ; ) \ - 1| + \\ < 2.
528. :
) = /42 - 4 + 1; ) = ^ + + 2 ;) = '2 - 2 + 1 + /2 + 2 + 1.
-
66
529. :
) }{) = ^(| - 2| + | + 2 |) ; ) /( ) = ^ ( | - 1 \ + \ + 1 |) ;
) / () = |3 - 1| + | - 4| - 2|2 - 1 |.
X " V530. ) = - , 8 (3 5).
) * = , 7 * (4 * 3).
531. :) ( , ) = 1; ) ( , ) = 1; ) ( | |, | |) = 1.
532. :) = \ - 2|;) = | 1| + 1;
) = | + 1|; ) = || | - 1|.
-
7.
533. () .) , ?
) ?) ?) .
40--
4 --
2 --
. . 533
. . 534
1 ( 500. ...),
-
68
534. .) .
) .
535. .
V III2 VIII V III4 V III5 6
4 4 3 11 6 8
) .) ?) .
536. - 2009/10 .
VII . VIII . I . II . III . IV . 15 8 31 33 33 28 34 42 75 70 89 280
) .
) , .
) :
VII . VIII . I . II . III . IV .
) .
-
7. 69
537. () ( ) .) ?) 10 ?
11--10--
. . 537 . . 539
538. ) ( ) -1 0 . 100, ?) 5, 10, 15 20. ?
539. 2006-2009. . .
540. : I: 216 , 205 , 201 , 186 , 182 ; II: 211 , 211 , 203 , 199 , 188 .
.
541. 32 :
7 8 10 7 - 6 9 13 5 1
.
-
70
542. 6 , 4 , , , . ? ( .)
543. : - 2310, - 3725; - 4011; - 2284 - 518. .
544. 300 ( );
0-5 5-10 10-15 15-20 20-25 35 65 120 70 10
.
545. 20 : 39, 40, 44, 42, 43, 39, 41, 41, 44, 45, 42, 43, 42, 42, 40, 44, 43, 42, 40, 43. .
546. 12 580 :
0-5 . 5-10 . 10-15 . 15-20 . 20-25 .
1220 910 5340 3750 1360
.
547. 30 - : 2, 5, 3, 4, 1, 7, 12, 9, 6, 11, 11, 6, 5, 1, 2, 3, 7, 7, 10, 14, 3, 2, 5, 7, 4, 11, 8, 7, 5, 1. .
-
8.
, 11 - 1 ( , )
, -
( + 1> = \ 2 + 62 2,
! , 1>\, \ , 2 , 62 , 2 ( ). (,) 0
\ + 612/0 = \ \ 2 + 2 = 2
.
1 = \12 2&1 0 (. ~2 2
(,)
_ \2 2&1 _ \2 2\\(>2 2 1 ^ \1>2 2 (>1
2 = 0 1&2 2\ \2 2\ / . 1 1 (. = ), .
2 2 2
-
72
3 = 0 - 2&1 = 2 - 2 = 0, :
) 2 , & , 2 , &2 , ( ). - , 0,
) = &! = 2 = &2 = 0 , 2 , ;
) = &1 = 2 = &2 = = 2 = 0, ( ) ( ,) , , 6 , .
.
8.1.
548. + 3 = 0. . ?
549. :
550. ( ) , :
) (3,1)
) (7,4)
-
8. 73
551. :
)
)
)
5 + 2 = 29 = 1
' 7 6 = 1 11 + = 12
= 5 ~ ( - 2 ) + 7 = - 7
3( 5) + 2 = 4 2 + = 12;
: + 4( - 1) = 3 + 2 = 3;
5 9 = 6 4( - 2) - 3( - 1) = 4?
( 552- 556):
552. ) + = - 6 , - 2 = 24; ) - = 5, - + 7 = 1;
) 2 + 4 = - 1 , + 7 = 2; ) 5 - = 17, 2: + 3 = 11;
) 4: + 5 = 25, 4 + = 13.
553. )' 4 - 5 = 3
2 = 11; ) (
) 7 26 = 36 5
. 2( - 6) = 8 + 6; ) {
)' 0,2 + 0,5 = 2
2 = -46 ; 5)
554. )
( -------- = 24 5
6 1- + - = + 1
1 6 + 4 +
' (3( + 1) + 5 (2 /- 2) = 30 2( + 2) 3{ 3) = 6;
)1( - 3)( - 1) = ( - 4)( - 1 )( + 2) = ( + 15)( - 6);
6 + 51 = - 7 45 + ^ = 4;
5 = 2 8 2(3 - 20) = 7;
3 54 ' + 6 = 9
1,3 - 2,1 = 3,6 2,1 + 1,3 = 15,2;
)( + 2) : ( + 5) = ( - 1) : ( + 1)
(2 - 5) : (2 + 2) = ( 4) : ( 1).
-
74
555. )
0
;
- 2)
+ 41, = 12;
7 + 2 6
7 + 3 6
( ~ 3) = 4
( + 2) = -3 ;
4 5 + 10 5 5 + 8 _ -
5 4 + 4 6 + 2/ 10
= -1
15.
556. )
)
4 10
( + )2 = ( 3)( + 3) + 10/
\ ( + 5)( - 5) = ( - 5)2 - 10;
( + 2)2 + ( ~ 2)2 = 2 + 2 \ (2 - )2 + ( - I)2 = 2 + 2;
( (2 - I)2 - 42 = 3
) \ ( 2)2 2 = 92.
( 557-561):
558. )
557. ) + 2 = 26, & = 3; ) 2 + = 12, + 6 = 3) 2 + = 5 , 4 + = 11.
2 3 = 0 = 16 ;
= 2 3 4 = 8;
2 = 1 \ 2 4^ / = 10; 45 + = 6 \ 35 - 2* = 4;
= 3 2 = 1;
2
559. )
) 5 2 = 29, 10 + 132/ = 24; ) 2 7 = 2, 6 112/ = 26;
)
)
)
)
560. ) )
)
+ 5 = 7 \ 6 + 10/ = 1;
2 + / = 10 + = 5;
= 6 5 - = 5;
2 + ^ /2 5 + 32/+ 2 = 0 2 = 1.
-
8. 75
562. :
1 .
2 - .
564. :
) 2 = 0, + 5.
565. + = 1, 2 + 2 = 5 . .
566. :
) = 2 + 4, = | - 2 ; ) 2 - = 4, = 2 - 1;
3) = - , 2 = 1.
5
567. , - :
) 2 + 5 = 0;
) + - 1 = 0;
) | + - 1 = 0;
) + 2 = 0.
563. :
) + 2 = 3, 2 = 1; ) 2 4, 2 = 0.
) 2 - = 5, 2 + = 3-, ) 2 + = 9, - = 0;
-
76
( 568-569):
. X V X V568. ) - + - = 2 , -------- = 0;
; 2 3 2 3) 6 + 5 = 2 6 + = ^
) + = 0,6, - = 0,3;
) ^ - | = 4, 0,5 0,2/ = 2;
, - 2 - 1 2 ) + - 5 - = 3^
569. ) + ^ 1 = , = - 1 -; 2 5 2 7 2
)^ + 4 , 2 / + 10 5 5
+ + 5 = - 3 , +5 + 3 ;
. 2 - + 15 2 5 7 - 2 + + 19 ~ 3 _ 3 2 + 3 ~ 2 = - ! ;
) 1 _ ^ = ^ [2_ 2(_ 7 ) _ ] 1 ^ _ ^ + ; + 1 8 = 1;
) 2 - 2 + 5 _ 5 - 6 = 1 ; % + 2 _ 2( _ 1) = ^ 2 .
. + 5 - 16 4 2 5 + 7 - 14 7 - 5 - 122 3 ~ 4 4 2 = 4 '
570. ----- ---------------- - ----- = 0 0,1 0,3 = 5, + .
571. ) 2 = 12 + 6 = + 2 7, + !) 5 + 2 = 25 42 4 = 6, + 2x1) 2 + 2 = 6 = 5, + 2 !
572.
( 3) + ( + 2)/ = 3 ( + 2) ( 1 ) = 1
573. 0,2 = + = (5, 7) ?
-
8. 77
574. ( -2 ,1 ) :
) + 2 = , 2 + -, ) - = , + = 2;) 2 - = - + , + \ = 2 + 4;) 4 + 7 = - , -2, - 2 = 2 - .
575.
) (2,2) .
) (*).
576. 54, 20. ?
578. 168, 6. ?
579. , 3.
580. 42. , 3 2. ?
581. , 2 2; , 2 8. ?
582. 13. 27. ?
583. 166 . , 2 16. ?
584. , 38 , 11 .
585. 20 . 4 , 2 , . ?
586. 54 , 5 : 1 1 . .
2 + / - 6 = 0, - 2 - - 1 = 0 . (*)
577. ?
12 - .
-
78
587. 8 , 16 2 . ?
588. 56 . 4 : 3 .
589. 12 . .
590. 10,5 . , , = 3 . .
591. , 8 , - . .
592. , , . : 7 , 8 1 1 .
593. , , 16 , 20 24 .
594. :) ;) 30 ;) 20% .
8.2.
-
595. + = 2.) :
(1,1), (2,0), (3 ,-1 ) , (3,1), ( - 2 , 4 ) , ( - 5 , 6 ) , (10,8);) ?) -
.
( 596-600):
596. ) \/2 + / = 5, 5/2 - 2 = 4;) /: + 2/2 = 3 \/ , \/2 + \/ = 5;) /2 = 2, = 1; ) /5 5 = /5, \ / 5 = 5.
-
8. 79
597. )20 (8 36) = 56 ( + 6 3)
12 - ( + 6 + 2) = 42 - (9 - 46 + 7);
( + 3)(/ + 5) = ( + 1.)( + 8)( 2 3)(5/ + 7) = 2(5 6)( + 1);
1 ( + 1 ) - 2 = 2( _ )
)
- ( ~2>) = 2 - .
1 : 2 = 0 + 1) : (9 + 4) 1 : 3 = ( - 1 ) : ( + 2);
(9 + + 2) : (1 + + ) = 4 : 3 (2 + 2 ) : (3 + 2) = 3 : 2 .
+ 3 8
{ - 1) : ( + 2) = 1 : 2 : = 4 : 3;
599. )
)
) -1 ; ) % 0. 201. ) { -3 ,-2 ,-1 } ; ) {-3, -2 ,-1 } .202. ) < 1; ) < 2; ) -3 ; ) > ) > -2; ) 12; ) < 5 . 203. ) ^ ) < . 204. ) 0; ) (-,
) (- , - ; ) (-,4). 205. ) 1, 2, 3, 4; ) 1, 2; ) 1, 2, 3, 4, 5, 6. 206. 13.
-
116
207. ^ 208. ) {1,2,3,4} ; 6 ) {1,2 ,3} ; ) 6 { 1 , 2 , 3 , . . . } ;7
) { 1 , 2 ,3 , . . . } . 209. ) < 2; ) > 1; ) > ) > 3;1 2
) - < < 2; ) 5 < < ) > 4. 210. ) < 2; ) > 6 ;3 3
) > 3. 211. ) > 3; ) > 6 ; ) > 2 . 212. ) > 4; ) > 2 ;) > 0; ) > 1,2; ) ^ 3. 213. ) ' ^ 3; ) > 1; ) ;
1 4) ^ 11. 214. ) > 2; ) > ; ) < - ; ) < 2. 215. = 1.1 0216. = 2 .
/^ 2,5. . 217
217. ) . . 2,5 < < 2;) ; ) 5 ^ ^ 7; ) - ^ ^ 0; ) ^ 50. 218. ) -
[5,+), ( , 17/3). 6 ( , 17/3) [5, +) = [5,17/3). ) 6 [1/2,+) ( , 4) = [1/2,4);) ( , 2/55)[2/55, +) = 0 , . ; ) 6 ( , 9/4)[ 2, +) = [-2 ,9 /4 ); ) ( - , -1/35) [-6 7 / 4 ,+) = [ 67/4, 1/35); ) 6 [7/39,+) (- ,2 [ = [7/39,2]. 219. ) = 1; ) 6 { 2, 1,0};) { 2 , 3,4}; ) 1 .
220. ) 2 ^ < 2; ) < 3 > 3. 221. ) 1 ^ 2 1 , 1 ^ ^ 3;) 1 < ^ 0; ) 3 > 5 3 < 5, . ( , 2) ( 8 , +);) ( , 3/5] 1 [1,+); ) ( , 1/6] 1 [3/2,+); ) 6 (2.3).222. ) ^ 1 : 2 + 1 > 5, > 2. < 1 2 + 1 > 5, . > 4; , < 1. , > 2. ) 6 ( 4/3,0); ) [ 3,5]; ) (5/3,3); ) = 2.223. {4,6 , 8 , 10}. I) + { 6 , 9 ,12,15}. 224. 3 < 2 - 5 < 17; 4 < < 11.225. / + 2 , . < 0 ,
. ^ 3 - 1 + - 3 > + 2, . ^ 6 . , ( , 2/3] 1 [6 , +). ) - 2 ^ < 5.
248. ) : 12 5 > 0 1 > 0; 2 2 5 < 0 5 5 5
1 < 0. > - > 1, . > - , < -
< 1, . < 1. ( , 1) (5/2,+).) ( 2 , 3); ) ( , 1 /2 ) [3, +); ) 6 ( 2 , 1 ].
2 5249. ) ---------------- 1 > 0, .
+ 3 8 -- ^ 0. : 1 ^ 8 , > 3; 2 ^ 8 , 0, . > 2; ) < - ; ) < -; ) < 5; ) 0, . 2 < < 3,
-
6. 133
+ < > ' 6 (_02) (3, +); ) 1 < < 2, < 1 > 2.
487. ) . . > 2, < 2. ) > 0 1 1
1 < ! !/ < 0 I > - ; ) > 0 < 1; < 0 > 1; ) > 0 1 1
< V < > - . 488. ) (2,1) - . ) - .489. ) = 0; ) = ) = - ;
2 3
X0 /2
-4/
. . 487
490. , 5 = + 3, >1(2,0) (0,4),
2 4 - = 4. 492. = 2 2.
-4(3,0), = 2 + 6
= -1 ; ) =
= 2 + 3 = 1. . 491. ,
493.
6.2
494. = 2, = 2. 495. = . 496. ) (0,1); ) (, | ) ; ) (0,-3);( 1\ 29 1 3
5/ 497- 6 = - - 498. ) < - ; ) > ; ) > 1. 499. ) < 0 < 2, = 0 = 2, > 0 > 2; ) < 0 < -4 , = 0 = 4, > 0 > 4. 500. . 501. ) ); ) ).502. ) = 4; ) = -1 ; ) & = 3. 503. = 3. 504. ) = 27; ) = 8.
9505. = - .
2
506. ) = 2 , = 2 = 0. = 2. ( .) ) = + 1 = 2 + 2 = 2. 4 6 = 10 = 4. ) = 3, = 2 . 2 = (4 6) 3 ( 2), = 2.
-
134
507. ) = 0 -, = 0 -. ) 3 + =( 12\
12 - (4, 0) ( = 0), - 5 10, I
( = 0). , + = 1, 12 1 4 , "
= 4 = 4.
12= 6 ,
508. () = + = 1, () = 2, = 0,() = 1, : 2 = + 1 = , = 1, = 1. 509. =2 5. 510. = ,
3
511. ) = + (2,0) 5(1,3). = + = 3, = 6.) (2,0) 5(0,1), = , = 1. ) = 1,5.
3 3512. ) = 2; ) 0 = - ; ) = 4. 513. (2, 2); 6 = - .5 2
514. 3 = ( 1) 1 4 + 1 = 1. 515. / ^ = + 1,
/ + !, /(2) = 4 + 1, /( /( )) = 2 + 1) = 4 + 3.
516. ) = 1. ) = - + 3 -
(4,0) 5(0,3). = = 6.4 21
517. ) : 1 = 2 = 1; ) = ; ) = ; )
/(2 + 1) = 6 + 2, /() = /(2 + 1) = 1; ) /(/( )) = 9 4, = 1; ) = 518. (0 ,-2) ,
-2 = ( 1) 0 + - , 11 519. ) 1 = I.
= + 1, /(4) = 2(1 + 1) 3 = 21 1. , ( ) = 2 1.
) () = = + ) () = 5. 520. . .
-
6. 135
. . 520
6.3
521. . . = =55 4 '
. . 522
522. ~ = 7 (). 523. = ------ = 5 (. ).
524. - 3 (). 9 4 -
- . 525. = - (). --------- =
-
136
14
-
6. 137
. . 527
528. ) == \2 - 1|; ) = | + 3 1; ) = \ - 1| + | + 111 X, 2, { /2, X 1,
529. ) / ( ) = - 2 < < 2, (). ) / ( ) = < 1/2, ~ 1 < < 1,1[ - , ^ 2, 1 ~ , ^ 1
3,
(). ) / ( ) =6 + 1, 2 + 5,- ,
< 1/3,1/3 < < 1/2, 1/2 ; < 4, ^ 4
().
) ) )
530. ) 8 (3 5) = 8 = 8 4
7 * = 7 * 6 = = 21. 531. . .
8 + 4 2
= 6; ) 7 * (4 * 3) =
) )-
__1
)
1
1
. . 531
-
138
532. . . ) = 2, 2 ,
' - - 1,
^ 2,< 2; 6 ) ' < 1,
( + 1, > 1, 1 1, < -1;
< , > 1, \ 2 , < 1; ) = + 2 7 = 2, = 7, + = 9. ) 21. ) 4. 572. = 0, = 5.
573. = -1 , = -12. 574. ) = 0, = -1 ; ) = -3 , = - ^ ; ) = 5,
= 2; ) = 2, = 3. 575. ) = 2, = 2, 2 4 : 1 = 0, = 3. ) . .
576. , + = 54, = 20, = 37, = 17. 577. 1 2. 578. + = 168 = 6
X = 6, = 24, = 144. 579. / = 3 = 3 V
9 3 = , = . 580. + / = 4 2 = / + 2 = 32, = 10.
581. . = 2 + 2 + = 2( ) + 8, . 2 = 2, = 8, = 22, = 10. 582. = 10 + . + = 13 10 + (10/ + ) = 27, = 8, = 5. 85. 583. 6 = 166 = 26 + 16 = 316, 6 = 150. 584. 8 . 585. 12 8 . 586. 10 ,22 , 22 . 587. 5 3 . 588. 2 + 26 = 56 : = 4 : 3 = 16 , 6 = 12 . 589. . 590. 1 2 9 . 591. \+ 2 = 8, \ 2 = 3; \ = 5,5 , = 2,5 . 592. \ = 2 , = 5 , = .593. , 5 7 . 594. ) 140 40; ) 75 105; ) 80 100.
-
142
8.2
595. ) : (1,1), (2,0), (3,-1),(2,4); ) ; ) . . 596. ) (/2, /3); ) (/2,/3); ) (/2,1 + /2); ) - . 597. ) (2,-3); ) (3,1); ) (-2,3). 598. ) (3,4); ) (6,8); ) (5,1/3).
5 - *> ( 4 > ( ! > >
600. ) (-2,5); ) ; ) (3,1); ) (3,2). 601. ) ; ) .
602. ) ( ~ , ^ , ) ; ) ( - 2 , > , - ) . 603. ) (4,4,8); ) (1, -2,3); ) (0,0,2).
604. ) : 1
112
+ - = 5. 2 6 = 0, 8 + 25 = 1
= , 6 = . + = 12, = 6 (9,3).
1 1) (5,1); ) (7,4). 605. ) - = - = 6.
+ 56 = 16, 5 36 = 4. = 6 = 2, = 2
2 = = - , ( , ). )1 1 1 112 ~9
) (5,1); ) (24,36). 606. ) = -3 , = 7; 6) = 2, = -5 ; ) = -2 , = 11.3
607. ) 2 1 = 0 = 1; ) = - ; ) = 0. 608. ) / , 12 38/ , 7. 609. 0 = 2, .
610. ) ; -- = 1 ; ) = ^(5 + ), = | - 5; ) = 2 - | V
= 3 ( - | ) ; ) = ^ 12) , = ^(5 + 12). 611. ) = 3.
612. ) () = + 3; ) () = -2 + 4; ) () = - - + 11. 613.
2 + 26 = 18 + 6 = 9. : (8,1), (7,2), (6,3), (5,4), (4,5), (3,6), (2,7) (1,8).
7777- 1 + + 10 2( + 10) 2 62 , 4 - , . -10. 2 = -10,
-
8. 143
. &1 \ , 4 3 3 = , . - = = -
02 2 2 23
. 3 = 10 ^ . ) 1 4
; 2 = 4 . ) 1 4 ; 2 = 4 . ) 1 ^ 6
2 3 ; 2 = 6 . ) 1 , 9
. , 6 ; 2 = 6 ^ -
; 3 = 6 = - .
615. ,& = 10 + 6. + 6 = 14 106 + = 10 + 6 + 1 8 . = 6, 6 = 8. 616. + = 9, 100 + =9(10+2/) + 18, = 54. 617. 10+/+8 = 77, 10+18 = 10+ = 53. 618. 10 + = 4( + ) + 3, 10 + + + = 28; = 23. 619. 10 + 1--------- = 5--------- 10+ = 10+ 9 = 5, = 6. + +
56. 620. 36. 621. + = 225 1 - + 1 - = 315 = 90, = 135
. 622. 252 186. 623. 48 40. 624. ~ ~ . 625. 1 1
1^ +2 = 70 2>1 = 6(2 ), = 30/ , = 40/ . 626. 16,8 / , 4 ,2/ . 627. /, /. 628. 6 = 7 2 62 = ( 6)( + 6) = 385, + 6 = 55, = 31, 6 = 24. 629. 1 + = 350, = 2 + 30 = 80, = 270. 630. + = 100, + = 32; = 85 ,
5 = 15 . 631. 204 , 84 . 632. , . + 5 = 2( 5) + 5 = 3( 5). = 11, = 13, + = 24 . 633. 7 30 . 634. 20 , 30 . 635. + = 713,4 2- = - ; = 155 , = 558 . 248 .5 9636. , 5 + 3 = 6 1 = , = 23, = 4.
637. 379 65 . 638. . 639. = 6,3
+ 7 = -( + 7) = 17. 640. + = 59, + = 55
+ = 51. 2( + + ) = 165, + + = 82,5. = 82,5 ( + ) = 23,5, = 82,5 ( + ) = 27,5 = 82,5 - ( + ) = 31,5 . 641. 5 + 8 = 340, 8 + 5 = 310 = 201, = 301. 642. 600 3 400 3.643. 1001 451.
-
144
8.3
644. ) 2 = 3 ( 3),
^, -- '''^ , \ {3}. )
; )( -2,3) ; ) ^ 1 , - 0 . 645. ) (, - 6); ) ( + 56, - 6);21 10& 206 9 \
; ) (2 6, + 4&).
2 _ __ ^ ^646. = - = ^ ^ = + 1 + - . ( 1) | 8
(0, -1 ,2 , 3, 5,9, -3 , -7}. = 0, = 1, = - 3, / = -7 , N 5 (2, 3,5, 9}. 647. ) (2 ,-1 ,-3 ) ; ) (1 ,-1 , 2); ) (5,6,10).
648. ) : 1 ^ 0, > 0; 2 0, < 0; 3 < 0, < 0 4 < 0, ^ 0. (2,1), (0 ,-3), (-6 ,9). ) (2,1), (8,13); )(-1,1) . .
649. ) ( )( + ) = 24, - < + , : 1 - = 1, + = 24; 2 - = 2, + = 12; 3 = 3, + = 8; 4 - = 4, + = . (7, 5), (5,1), . ) (53, 52), (19,16), (13,8), (11,4).
650. 11 + 8 = 73 ^ ^ . = 1 = 5 , = 3 = 5.
651. + 2 /2 = ( )( + ), : (1) ~ = 1, + 3 = 1; (2) = 1, + 3 = 1. (1,0), (-1,0).
652. ) 19 . 1999 - (1900 + 10 + ) =1 I . , 89 21 + 9 + + /, = . 0 ^ , ^ 9, = 7,
= 6. , 1976. . ) 1856. .
653. = . + 5 + = 1 0 + = 6 + 8, 2& + 8 = 10, . 6 = 1 , + = 9 (*). , 100+ 106 + (100+ 106 + ) = 99 99( ) = 99, . = 1 (**). (*) (**) = 5, 6 = 4. , = 514.
654. = - / + 2) = - , \ V
-
8. 145
= / + 2/() = . () + 2 / = ,
/ (;) + 2/() = 1 , /() =
655. = ( + + I)2 + 2( + I)2 + 1 1 = - 1 , = 0 .
656. ) ( + 2)2 2 = 48, .( + 2 + )( + 2 ) = 48. 48 : 1-48, 2-24, 3 16, 4-12, 6 - 8 , 8 -6 ,12 4, 16 3, 24 2, 48 1, (-1) (-48), (-2 ) (-24), (-3) (-16), (-4) (-12), (-6) (-8), (-8) (-6), (-12) (-4), (-16) (-3), (-24) (-2) (-48) (-1). : (11,-11), (6 ,-4), (5 ,-1), (5,1), (6,4), (11,11), (-15,11), (-10,4), (9,1), (9,-1 ), ( 10,-4) (-15 ,-11). ) ( + I)2 - 2 = 5, . ( + 1 + )( + 1 - ) 5. : (-4 , -2 ), ( - 4 ,2), (2 ,-2) (2,2).
9 9^ 7 2 657. 2 + 210, = ; = 60/ , = 80/ . 658. 3 6 /
8 40 / .
659. ( ). + 50 = 40-50, + = 60-30, = 1500, = 10. 1500 + 10(1 =
-
146
.664. , . ,
1 1 1 1 1 1 1 . 1 = - + =X X X = = 10.
9.
9.1
665. = 1682. 666. ) = 2, V = 973; 6) = 902,V = 10073; ) = 2/3(2 + \/3 ) 2, V = 3; ) = 67(1 + \/2 ) 2,V = (2 + /2)3. 667. = , = 264712, V = 5763. 668. = = 972, = . ) = ---- = 5; 6) V = 2 =2 27 / '45 3. 669. = 8 , V = 628 3. 670. ) 2 = 8; 6) = 15272. 671. ) 2 20 ; 6) = 40072. 672.'; = 5; ) = 15 , =2002; 6) = 8 , = 1302. 673. = 4 , = 4 , V = 643.674. = 2&7 + 2627 = 572, V = &27 = 483. 675. ) = ;6) = 4.
676. ) 8 4 = 32 2; 6) 1 12 3 = 2; 2 6 - 6 = 36 2. 677. 152.678. 50 . 679. = 57. 680. ) 2 = 12 = 12 ,
0 432 16 = , V = ---- 3; 6) V = 3. 681. : = 2 : 2 = .7 7 7682. = 4 , = 10 , = 8072, V = 1603. 683. = 4 , = 7 .
684. = 20 , = 6 = 600 , V = 2 = 240 00073 = 240713 = 2401 753,61. 11 = 1 13 = 1000 3.
685. , . (27)2 = 132 52 = 144,
12 6 72 = = . = 2( + ) = 60 + 2 2 7 7
180V = 2 = ---- 3. 686. = 2. 7
(2)2 = 144 = , = 12 , = 2172, V = 43273.V, 4 687. -4- 2 1
688 . 2 2 2 = 4. 689. 5,522 17,33 2.
690. - , , 0 : = 4. 691. 50%.692. 1713.
-
9. 147
693. 14 = 3 = 2744 3,
= = 7 = 14 , 14 = 2 = 22
49 14 = 2156 3. 2744 2156 = 588 3 .
2744 : 100 = 588 : . = 21,43%.694. 3. 695. V = 23. 696. 4,5. 697. 7. 698. ( + I)2 = 2 + 52 = 12 , = 72,52 V = 753. 27 , 699. 10,6 3. 700. = 10 , = 30 ,
V = 3, 30% V = 9003 2,8261.
9.2
701. 2. 702. ) ~ 3; ) 9 3; ) ~ 3. : - 360, V = 2 = 273. 90, 120, 180 , , . 703. V =3- 2 = 13503. 704. . 705. . 706. = 827, V = 23.
707. ) 1 : 1; ) 8 : 5; ) 8 : 5. 708. = 2 2 + 2 = 913002, 182 600 = 182,6 . 709. V = 2 = 10 3, ~ 27946. 710. V = 2 ~ 31 4002 3, ~ 279,^ 462, 2 0,04294
50 2 0,414 . 711. 2 = 50, = 3,98 . 47
).
1 1 99712. V = - 2 - 22 ~ 3,5 = 22 3.713. = 10 (), V = 20 30 300 102 300 = 30 000(6 ) 3 85 800 3.
714. = 2 , = 22 + 2 = 322. 715. = 62. 716. - () = = = 2/3,
*^7 * 120 V
= ------ = 4 - ^ ( = - = /).
= 2 = 4%/, V = \ = (16/3 36) 3.
-
148
. . 717
717. ().
= \02 2 - 2 = - = ^ 4 4 2
3/2 ^ , ^2 37
718. = \/2 + 2 = 5 , = =
+ 6 + = 1 , = 2 27 + 2 =
182, = 2 = 83 . 71 9. 2072. 720. 12^/52. 721. = + + = + \( + )2 2 + = 18 ().
. . 721
722.^2
2
723.
')" (). " " ' ' :V, = 2 '" = 2000/3 .
1000\/3 ,V - = 2500--------- 6039 3.^ 3
-
10. 149
10.
10.1
724. ) = 5; ) = 13 ; ) 5 = 17 ; ) = 5 \/2.725. ) = 4 , = 2472, V = 1273; ) = 1, =
2\/2 7(/ 2 + \/3 ) 2, V = -73; ) = 5 , = 9072, V = 10073;
) = 10 , = 972, V = 973. 726. = , = 97(12.727. 5, = 27 + 75 = 30072, V = - 2 2407 3.
728. ) V = 273; ) 12073. 729. = 31, = 41. 5 = \/2 + 2 = 51, 607 = 31 51 7, 1 = 2. , = , = 8 = 972 . 730. 13572. 731. 72 = , = 3 .
^ 7 = 157 = 5 , = 4 = - = 1273.
5 , 732. 2 13 = 26 2. 733. = 422. 734. 5-216 2----------- = 247 = , = 4 V = -------= 127 .180 3
735. 7( + ) = 967 2 + 10 96 = 0, . ( 6)( +16) = 0,
( > 0) = 6 . = /2 2 = 8 , V = 2 = 97 3.
736. ) = 4 , = 12 , ) 5 , = 60 2. 737. 2 7 ________ 25
= ^ = 0 = > 5 = V 2 + 2 = , = 572
V = 4973. 738. = 50(1 + \ / 2 ) 2, V = 7 3. 739.
= = \ 2. 817\/2 = = 2/ 2 = 9 , = 817(1 + \/2) 2 V = 24373. 740. = - = 9 2,
= = , V = ^ 2 = 973. 741. ) = , = 3\/3,
= , = 2772, V = 97\/3. ) = 10872, V = 72\/3.
742. ) = - = = - \/3 = 3\/3 (), = 97(3 +
2 \/3 )2 V = 2773. ) = 7 1
3 \ /2 , = 18(1 + \ / ) 2, V = 18^277 3;
) = - = , = 2 + ^ = 3 \ /3 , =
2772, V = 9 \ / 3.. . 742
743. = 81(1 + /2) 2, = 2433. 744. = 6(6 + ^ ^ 2,V = 247\/3. 745.
-
150
. : 5 = , -
: = = 3\/3. ,2 , = ( + ) = 2772, V = 2 = 97\/3,
= . 746 . 2 . 747 . ) = 2 ; ) = 172.
748 . , - , . , 5 = 4 2^ 7
= 2 7, = 1 . = /2 2 = ,
= 7( + ) = 572, V = 27 = - !
749. 5 = = 6 , 2 \ = 7, 7 3
1 = - = . = ^ + = - 2 = 2 7 2, ^ 4\ 1 2
V = - \ = - /2 - \ = 9 \/3. 750. = \/7, 5 = 8\/7,
= 63 2. 751. , . .
752 . 2 7 = 18 = 9 . 45, . \/2 = 2 5 = 9\/2. = \ 2 2 = 9 ,
= ( + ) = 81(1 + \/2) 2, V = 2 = 243 3.753 . 30.
10.2
__ 57754 . = 2 7
60. 755 . 4 : 1.
8 7 2 ^ 27 27
757 . = 3, 5 = \/2 + 2 = \/92 + 2 = \0.
__ 27 __ 1 / 5 5 10
^58. = 2 : 3. 7 59 . = 2, V = /553. 7 60 . .
761 . 7 > 27 5 > .
-
10. 151
762. = 247 - 157 = 972, = , = 5 . 2 =
> = 180 = 216. 763. V = ~ 0,018843, ~180 ^ 5 3
19,3 0,01884 0,3636;. 764. V = 6473, 160,77. 765. = /2,^
V = (2 - /3) 3. 766. = .
767. = \/2 + &2 = 25 (). , = . - 12
V = = 12003. 768. ) 1 : 1;
) 3 : 4; ) 2 : 3. 769. = , 2 = 4 , = 2 = 5 , \ 4 , 2 = , 1\ =2 7^ = 3072, 2 = 2275 = 4072, =
., %2- 247 3, 1/2 = 2 = 273.
5770. = (5 + \/2) 2, = 3.
/- \/3771. 62 + 3 2\/3 = 6 + 3+3 = 1 . = - + 3 = - ^ -
= , V = ------- = - 3. 772. ( = \ + 2)\ 3 4
27 21
' + 2 -2! + 27 2 + 2)3 3 3
= 3.
14773.
2
-
152
. . 779
779. , \/2 ()
---- \/2 22 = 2. ----- = -----------/2 ^ 2
] = ,
13
2
7 3\ / 2 43 ^\/2 '
780. # = 3*, 5 = 51 = / (5 )2 - (^)2 = 4$, - =
1287 I3 = 8, . 1 = 2. , = 8 , = 10 , = 27+78 = 14472.
781. , , V, 3, , ,
, 2
2 =2 \/2 7 2 : 7V*
, : V! = \ /2:6.782. - / 2 V3, - . - : = 227\/5, V = 37.783. V = 73. 785. = 2472. 786. (). = 8 , = /102 82 = , = /2 + 2 = 9
= ^ ' = 72 2.
. . 786
-
11. 153
11.
11.1
787. ) ( ), ( ) . ) ( ) . ) ( ) ( ) . 788. ( . ). 789. ) ; ) ; ) . 790. \. 2 = 2 2 \ = 12 , 14472.
792. 42 = 7 = , = 97 2, = 27 = 7 . 793. = , V = 367 3. 794. 27 = 127 = = 427 = 1447 2. 795. ) 427 = 17
) = 12, V = 20343; ) = , V = 97273.
5007796. , = 10072, V = 3. 797. = , =
2. 798. 6, = 2 + 7,52 = 12,5 . 799. = 12 . 800. =
801. 125%. 802. 4( + 1)27 = 427 + 87 = - .
803. ,
11.2
1
-
154
805. .
; = = 3 3
( + ) 9 [ 4 16'
= 2, = = \ /3.
806. = 7 . : 6 : = 2 : 3 : 6, 2 + 2 + 2 = 42 = 4 , 6 = 6 = 12 , = 288 2 V = 288 3.
807. V* = - 2 = - 37, 1 = ^ 37, = 2 = 3,
1 2 1 2 : : = - 3 : - 3 : 3 = - : - : 1 = 1 : 2 : 3 .
808. = 9 , = , = 7 .4 , 4 : V = -
1544
3~ --
16163. = = 1616 9 = 14544 = 14,544.
809. = = 4 , - = - 3 = 128
810. . , ,
\ /3 : , = = 9 ,
4 ^ = / \ 3 = / 3 = _ _ = 4 _ \-2 [/ / 9 '3 2
/811. = - , 2 = , = 42 + 4% = 4 2. 812. ) . ) .
813. 2 = 10 5 = \2 2 = 13 ().
= 60 2. = + , = , V 3 7 4000
81
-
11. 155
. . 813
814. (). 0 \ = = 1 ,
. = 0 \
= /7 .
1 ,
2 = \/2
815. , , 5, , , ().
: 8 = : ( - ), . 5 = ( - ) (1). = 1
442 = 2 + (2). 5 (1) (2)
2 . ( + 412 = ? + ( )
- 2. 443 = 2, ^ -------
243
1 =1- - '
816. ^ 817. 48 \/3. 818. = / (2 - ) . 819. 4 12
: 2 ( )
= = 3\/ V :2 - 297 ' / = 3
820. () 2 + 2,
= - ^ = = = = .
-
I156
821. (). - \
= 2 - 2'
_ II ~ / ( ~ 2 ) 1
822. - . () 5 ,
-
11. 157
826. : = ^ (^\/3 = ^/, = 2 = ^/, :
)
2- ^ + - ^
4(2-VI
\ /3
9\/327
9\/3 2
827. , , , ( - ). 2. /2 ( -, ). , , , I) , (1 + \/2), (2 + \/2).
828. = = 3 \/3 2
= \/3 = 9 = = . 2
V*. | 27# 9
/ = ~ | 3 4 '
829. ) 5, , , , , . . . (). , 3 0 , , , . . . , 5 = = = . ) 3 0 , , , . .. , , , ... (. 62) 30, 3 0 . + 30, + 3 0 , + 30, ... , , , ... ( 30). = = = , , , ... .
1. 2. , 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.