Найдите все малочисленные решения уравнения:

а) (2x-y) (x+2y) = - 3

б) 2x^2+xy-y^2 = - 3

a) (2x - y) (x + 2y) = - 3

1) 2x - y = 3 = > y = 2x - 3

x + 2y = - 1 = > x + 2 (2x - 3) = - 1 = >

x + 4x - 6 = - 1 = > 5x = 5 = > x = 1

y = 2x - 3 = 2 - 3 = - 1.

Первое решение (x, y) = (1, - 1)

2) 2x - y = - 3 = > y = 2x + 3

x + 2y = 1 = > x + 2 (2x + 3) = 1 = >

x + 4x + 6 = 1 = > 5x = - 5 = > x = - 1

y = 2x + 3 = - 2 + 3 = 1.

Второе решение (x, y) = (-1, 1)

3) 2x - y = 1 = > y = 2x - 1

x + 2y = - 3 = > x + 2 (2x - 1) = - 3 = >

x + 4x - 2 = - 3 = > 5x = - 1 = > x = - 1/5 - нецелое.

4) 2x - y = - 1 = > y = 2x + 1

x + 2y = 3 = > x + 2 (2x + 1) = 3 = >

x + 4x + 2 = 3 = > 5x = 1 = > x = 1/5 - нецелое.

Всего два решения (x, y) = (1, - 1) и (x, y) = (-1, 1)

б) 2x² + xy - y² = - 3

x² - y² + x² + xy = - 3

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

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

(x + y) (2x - y) = - 3

1) x + y = 3 = > y = 3 - x

2x - y = - 1 = > 2x - 3 + x = - 1 = >

3x - 3 = - 1 = > 3x = 2 = > x = 2/3 - нецелое

2) x + y = 1 = > y = 1 - x

2x - y = - 3 = > 2x - 1 + x = - 3 = >

3x - 1 = - 3 = > 3x = - 2 = > x = - 2/3 - нецелое

3) x + y = - 3 = > y = - 3 - x

2x - y = 1 = > 2x + 3 + x = 1 = >

3x + 3 = 1 = 3x = - 2 = > x = - 2/3 - нецелое

4) x + y = - 1 = y = - 1 - x

2x - y = 3 = > 2x + 1 + x = 3 = >

3x + 1 = 3 = > 3x = 2 = > x = 2/3 - нецелое.

Второе уравнение не имеет решений в целых числах.