2. Решите уравнения: а) 3x² = 15 х; 6) 100 x² - 25 = 0; B) 2x²+ 3x + 1 = 0; г) 4x² - 11x + 6 = 0.

а) $$3x^2 = 15x$$

$$3x^2 - 15x = 0$$

$$3x(x - 5) = 0$$

$$x_1 = 0, x_2 = 5$$

б) $$100x^2 - 25 = 0$$

$$100x^2 = 25$$

$$x^2 = \frac{25}{100} = \frac{1}{4}$$

$$x = \pm \sqrt{\frac{1}{4}} = \pm \frac{1}{2}$$

$$x_1 = \frac{1}{2}, x_2 = -\frac{1}{2}$$

в) $$2x^2 + 3x + 1 = 0$$

$$D = 3^2 - 4 \cdot 2 \cdot 1 = 9 - 8 = 1$$

$$x_{1,2} = \frac{-3 \pm \sqrt{1}}{2 \cdot 2} = \frac{-3 \pm 1}{4}$$

$$x_1 = \frac{-3 + 1}{4} = \frac{-2}{4} = -\frac{1}{2}, x_2 = \frac{-3 - 1}{4} = \frac{-4}{4} = -1$$

г) $$4x^2 - 11x + 6 = 0$$

$$D = (-11)^2 - 4 \cdot 4 \cdot 6 = 121 - 96 = 25$$

$$x_{1,2} = \frac{11 \pm \sqrt{25}}{2 \cdot 4} = \frac{11 \pm 5}{8}$$

$$x_1 = \frac{11 + 5}{8} = \frac{16}{8} = 2, x_2 = \frac{11 - 5}{8} = \frac{6}{8} = \frac{3}{4}$$

Ответ: a) 0, 5; б) 1/2, -1/2; в) -1/2, -1; г) 2, 3/4