749. Решите уравнение и выполните проверку: a) $$x^2 - 2x - 5 = 0$$; б) $$x^2 + 4x + 1 = 0$$; в) $$3y^2 - 4y - 2 = 0$$;

a) $$x^2 - 2x - 5 = 0$$ $$D = (-2)^2 - 4 * 1 * (-5) = 4 + 20 = 24$$ $$x_1 = \frac{2 + \sqrt{24}}{2} = \frac{2 + 2\sqrt{6}}{2} = 1 + \sqrt{6}$$ $$x_2 = \frac{2 - \sqrt{24}}{2} = \frac{2 - 2\sqrt{6}}{2} = 1 - \sqrt{6}$$ б) $$x^2 + 4x + 1 = 0$$ $$D = 4^2 - 4 * 1 * 1 = 16 - 4 = 12$$ $$x_1 = \frac{-4 + \sqrt{12}}{2} = \frac{-4 + 2\sqrt{3}}{2} = -2 + \sqrt{3}$$ $$x_2 = \frac{-4 - \sqrt{12}}{2} = \frac{-4 - 2\sqrt{3}}{2} = -2 - \sqrt{3}$$ в) $$3y^2 - 4y - 2 = 0$$ $$D = (-4)^2 - 4 * 3 * (-2) = 16 + 24 = 40$$ $$y_1 = \frac{4 + \sqrt{40}}{6} = \frac{4 + 2\sqrt{10}}{6} = \frac{2 + \sqrt{10}}{3}$$ $$y_2 = \frac{4 - \sqrt{40}}{6} = \frac{4 - 2\sqrt{10}}{6} = \frac{2 - \sqrt{10}}{3}$$