521. Решите уравнение: a) x² - 5 = (x + 5)(2x - 1); 6) 2x - (x + 1)² = 3x² - 6;

521. Решите уравнение:

1. a) $$x² - 5 = (x + 5)(2x - 1)$$ $$x^2 - 5 = 2x^2 - x + 10x - 5$$ $$x^2 - 5 = 2x^2 + 9x - 5$$ $$x^2 - 2x^2 - 9x - 5 + 5 = 0$$ $$-x^2 - 9x = 0$$ $$-x(x + 9) = 0$$ $$x_1 = 0$$ $$x + 9 = 0$$ $$x_2 = -9$$
2. б) $$2x - (x + 1)² = 3x² - 6$$ $$2x - (x^2 + 2x + 1) = 3x^2 - 6$$ $$2x - x^2 - 2x - 1 = 3x^2 - 6$$ $$-x^2 - 1 = 3x^2 - 6$$ $$-x^2 - 3x^2 = 1 - 6$$ $$-4x^2 = -5$$ $$4x^2 = 5$$ $$x^2 = \frac{5}{4}$$ $$x_1 = \sqrt{\frac{5}{4}} = \frac{\sqrt{5}}{2}$$ $$x_2 = -\sqrt{\frac{5}{4}} = -\frac{\sqrt{5}}{2}$$

Ответ: a) $$x_1 = 0$$, $$x_2 = -9$$; б) $$x_1 = \frac{\sqrt{5}}{2}$$, $$x_2 = -\frac{\sqrt{5}}{2}$$