Question

решите уравнение:
(y+x)^2-16=x^2(x+12)

Answer 1

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

y^2 + 2xy + x^2 - 16 = x^3 + 12x^2

x^3 + 12x^2 - y^2 - 2xy - x^2 + 16 = 0

(x-2)(x+4)^2 - (y-x)(y+x) = 0

(x-2)(x+4)^2 = (y-x)(y+x)

y = x или y = -x

x = 2, y = 2 или x = -4, y = -4