Question

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

Answer 1

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