Помогите с системой! x^2-y^2-xy=2

x+y=-2

2xy=?

{ (x - y) (x + y) - xy = 2

{ x+y = - 2; y = - 2 - x = - (2 + x)

Подставляем

-2 (x - y) - xy = 2

-2x + 2y - xy - 2 = 0

-2x - 2 (2 + x) + x (2 + x) - 2 = 0

-2x - 4 - 2x + 2x + x^2 - 2 = 0

x^2 - 2x - 6 = 0

D = 2^2 + 4*6 = 4 + 24 = 28 = (2√7) ^2

x1 = (2 - 2√7) / 2 = 1 - √7; y1 = - 2 - x = - 3 + √7

2xy = 2 (1 - √7) (-3 + √7) = 2 (-3 + 4√7 - 7) = - 20 + 8√7

x2 = (2 + 2√7) / 2 = 1 + √7; y2 = - 2 - x = - 3 - √7

2xy = 2 (1 + √7) (-3 - √7) = 2 (-3 - 4√7 - 7) = - 20 - 8√7