3) (x²−x)² - 10x(x² -1) +9x² = 0;

Решим уравнение:

$$(x^2 - x)^2 - 10x(x^2 - 1) + 9x^2 = 0$$

$$(x^2 - x)^2 - 10x(x - 1)(x + 1) + 9x^2 = 0$$

$$x^2(x - 1)^2 - 10x^2(x + 1)(x - 1) + 9x^2 = 0$$

$$x^2[(x - 1)^2 - 10(x + 1)(x - 1) + 9] = 0$$

1) $$x^2 = 0$$

$$x = 0$$

2) $$(x - 1)^2 - 10(x + 1)(x - 1) + 9 = 0$$

$$x^2 - 2x + 1 - 10(x^2 - 1) + 9 = 0$$

$$x^2 - 2x + 1 - 10x^2 + 10 + 9 = 0$$

$$-9x^2 - 2x + 20 = 0$$

$$9x^2 + 2x - 20 = 0$$

$$D = 2^2 - 4 \cdot 9 \cdot (-20) = 4 + 720 = 724$$

$$x_1 = \frac{-2 + \sqrt{724}}{18} = \frac{-2 + 2\sqrt{181}}{18} = \frac{-1 + \sqrt{181}}{9}$$

$$x_2 = \frac{-2 - \sqrt{724}}{18} = \frac{-2 - 2\sqrt{181}}{18} = \frac{-1 - \sqrt{181}}{9}$$

Ответ: $$x_1 = \frac{-1 + \sqrt{181}}{9}$$, $$x_2 = \frac{-1 - \sqrt{181}}{9}$$, $$x_3 = 0$$