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18.03.2013

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xy + 3x - 5y = -3 .

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. , , :

x(y + 3) - 5y = -3;

x(y + 3) - 5y -15 = -18;

(x - 5)(y + 3) = 18.

:

, (x; y) - (6; -21), (-13; -2), (4; 15), (23; -4), (7; -12), (-4; -1), (3; 6), (14; -5), (8; -9), (-1; 0), (2; 3), (11; -6).

: (x; y) (6; -21), (-13; -2), (4; 15), (23; -4), (7; -12), (-4; -1), (3; 6), (14; -5), (8; -9), (-1; 0), (2; 3), (11; -6).


4x3 - 2y3 - z3 = 0 .

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, , , .

, . - .

4x3 - 2y3 2, z3 2. z = 2z1, z1Z.

, :

4x3 - 2y3 - 23z13 = 0;

2x3 - y3 - 4z13 = 0.

, 2x3 - 4z13 2. - y3 2. y = 2y1, y1Z.

2x3 - 23y13 - 4z13 = 0;

x3 - 4y13 - 2z13 = 0.

, x3 2. , x = 2x1, x1Z, :

23x13 - 4y13 - 2z13 = 0;

43x13 - 2y13 - z13 = 0.

? , (x; y; z) . (x1; y1; z1), 2, . , 2.

, , 2. , 0. , x = y = z = 0.

: x = y = z = 0.


3.

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x 3 : 0, 1, 2. :

x = 3k (kZ).

x2 = (3k)2 = 9k2. .. 0.

x = 3k + 1 (kZ).

x2 = (3k + 1)2 = 9k2 + 6k + 1. , 3, 1, 1 3.

x = 3k + 2 (kZ).

x2 = (3k + 2)2 = 9k2 + 6k + 4. , 3, 1, 1 3.

, 3 0 1.

: 0 1.


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