Решите систему уравнений: {x²/y+y²/x=18, x+y=12 Ответ в уч.: (4; 8), (8; 4)

X + y = 12

x^2/y + y^2/x = 18

x^3 + y^3 = 18xy

(x+y) (x^2-xy+y^2) = 18xy

12 (x^2-xy+y^2) = 18xy

2x^2 - 2xy + 2y^2 - 3xy = 0

x^2 - 5/2xy + y^2 = 0

x^2 - (2 + 1/2) xy + (2 * 1/2) y^2 = 0

(x - 2y) * (x - y/2) = 0

x + y = 12, x = 2y - > x = 8, y = 4

x + y = 12, y = 2x - > x = 4, y = 8