решите уравнение х^4=(х-6)^2

Question

решите уравнение х^4=(х-6)^2

Answer 1

X^4 = (x-6)^2
x^2 = |x - 6|
x >=6 -> x^2 = x - 6 -> x^2 - x + 6 = 0 -> (x - 2)(x - 3) = 0 -> x = 2, x = 3 - не подходит (x > 6)
x < 6 -> x^2 = 6 - x -> x^2 + x - 6 = 0 -> (x - 2)(x + 3) = 0 -> x = 2, x = -3 - подходит

--> x = 2, x = -3