1

6 -2011

6 , . , .

: ; ; .

I. .1) : 32 8 162 = 19

:(3x + 4y)(x - 4y) = 19

19 : 1*19; 19*1; -1*(-19); -19*(-1)

: 3 + 4=1 3 + 4=19 - 4=19 - 4=1

3 + 4= -1 3 + 4= -19 - 4= -19 - 4= -1 , : (5;1) (-5;-1).

2) , 45. : 2 - 2 = 45. : ( )( + ) = 45. 45, : 1*45; 3*15; 5*9. :

= 1 = 3 = 5 + = 45 + = 15 + = 9

, :(22; 23), (9;6) (7;2).

3) :2 - 3 + 22 = 3. : ( )( 2) = 3. 3 :1*3; 3*1; -1*(-3); -3*(-1). : = 1 = 3 2 = 3 2 = 1

= -1 = -3 2 = -3 2 = -1 , :(-1; -2), (5; 2), (1; 2) (-5; -2).

II. 1) : 2 2 + 22 = 4 : ( - )2 + 2 = 4.

, , -2 2, .. = 2, 1, 0.

= -2 : ( + 2)2 + 4 = 4 => = -2.

= 2 : ( 2)2 + 4 = 4 => = 2.

= 1 : ( 1)2 + 1 = 4, ( 1)2 = 3 .

= 0 : 2 = 4 => = 2.

, :(-2; -2), (2; 2), (2; 0) (-2; 0).

2) : (11 + 6 8)(6 + 8 1) = 100. : (11 + 6 8) 9 (6 + 8 1) 13. 9*13 > 100 => (11 + 6 8)(6 + 8 1) = 100 .: .

3) : (3 + 5 7)(5 + 4 + 11) = 20. : (3 + 5 - 7) 1 (5 + 4 + 11) 20 => : 3 + 5 7 = 1 5 + 4 + 11 = 20.

, : = 1 = 1.: (1; 1).

III. 1) : 222 + 2 = 142 + 25. 2: , (22 + 1) 0, : 1, 2, 3, 6, 9, 18. (22 + 1) = 1, = 0. (22 + 1)=2, (22 + 1)=6, (22 + 1)=18, . (22 + 1) = 3, = 1. (22 + 1) =9, = 2. ) = 0, = 5; ) = 1, ; ) = 2, = 3; ) = -2, .: (0; 5), (0; -5), (2; 3) (2; -3).

2) : 222 + 2 - 62 10 = 0.222 + 2 = 62 + 10. 2:2 =
(22 + 1) : 1, 7. (22 + 1) = 1, = 0 (22 + 1) = 7, = 0,

: .

: 2 22 = 1; 2 3 + 22 = 3; 52 + 8 42 = 17; 2 + 2 + 2 = 4;(51 4 7)(31 + 2 6) = 68;(13 + 3 -2)(2 8 13) = 11;2 = 2 + 2 + 8;22+22-32=7;

9) 32+422-82-12=0;10) 122-422+72=9;11) 82+22-32=32;12) -242+322+42=48;13) 32+722=212+27;14) 7 3 + 6 5 = 0.

: ax+by+c=0, a b , , . .

, ax+by=c (1), .

, (0, 0) , .. ax0+by0+c=0 (2).

ax+by=c , (, ) -. a, b, c x0 y0, , .

(1) (2), : ax+by+c-ax0-ay0-c=0,a(x-x0)+b(y-y0), y-y0=

. a b , (0-) b, .. =0-bt. : =0+at. : x=x0-bt (3), y=y0+at (4),

t . , (3) (4) (1). (1) : ax+by+c=

= a(x0-bt)+b(y0+at)+c= ax0-abt+by0+abt+c= ax0+by0+c=0. , , (3) (4) (1).

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ax+by+c=0, - . . , :

.

. (

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), , a d b l : ad-bl=1. , , .

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a1=

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a2=

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a3=

=4+

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a4=

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a5=

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:

=

: [0; 4, 2, 4, 1, 1, 6].

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( 0). . - .

- , , , . , .

n-

, ( n2):

Pn=Pn-1an+Pn-2;

Qn=Qn-1an+Qn-2.

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87x+32y+5=0.

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2

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(

). :

-

=

. 877-3219=1. (-5):

87(-35)+32(95)+5=0.

, x0=-35, y0=95. x y :

x=-35-32t, y=95+87t.

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:3+2=7;3=2+8;17+34=153;+12=7;19+23=874;17+31=527;12-3=21;13-26-13=0.

:(1; 0), (-1;0); (-1; -2), (1; 2), (-5; -2), (5; 2); (3; -1), (3; 7), (-3; 1), (-3; -7), , +=2 += -2.(2; 6); ;(-4; 2), (4; 2), (-4; -4), (4; -4); ; (2;0), (-2;0); ; (-2;0), (2; 0); (2; 3), (2; -3), (-2; 3), (-2; -3); (-3;0), (3;0); (-7; 2).

( ): =1-2t, y=2+3t; 2) x=2-3t, y=4-2t; 3) x=5-2t, y=2+t; 4) x= -5-12t, y=1+t; 5) x=23-23t, y=19+19t; 6) x= -31t, y= 17+17t; 7) x=2+t, y=1+4t; 8) x=5+2t, y=2+t.