Решите уравнение:x^3-2x^2+x=(x^2-2x+1)^2

[latex]x^3 - 2x^2 + x = (x^2 -2x + 1)^2\\ x(x^2 - 2x + 1) - (x^2 -2x + 1)^2 = 0\\ (x^2 - 2x + 1)(x - (x^2 - 2x + 1)) = 0\\ (x^2 - 2x + 1)(-x^2 + 3x - 1) = 0\\ (x^2 - 2x + 1)(x^2 - 3x + 1) = 0\\1) x^2 - 2x + 1 = x^2 - x - x + 1 =\\= x(x - 1) - (x - 1) = (x - 1)(x - 1) = (x - 1)^2 = 0[/latex] [latex]x_1 = x_2 = 1\\ 2) x^2 - 3x + 1 = 0\\ D = 9 - 4 = 5\\ x_1 = frac{3 + sqrt{5}}{2}\\ x_2 = frac{3 - sqrt{5}}{2}\\ mathbb{OTBET:} x_1 = 1, x_2 = frac{3 + sqrt{5}}{2}, x_3 = frac{3 - sqrt{5}}{2}[/latex]