2. Решите уравнения: а) 4 х² = 16 х; 6) 81 x² - 36 = 0; B) 2x²+ 5x + 2 = 0; r) 3x² + 11x + 6 = 0.

а) $$4x^2 = 16x$$

$$4x^2 - 16x = 0$$

$$4x(x - 4) = 0$$

$$x_1 = 0, x_2 = 4$$

б) $$81x^2 - 36 = 0$$

$$81x^2 = 36$$

$$x^2 = \frac{36}{81} = \frac{4}{9}$$

$$x = \pm \sqrt{\frac{4}{9}} = \pm \frac{2}{3}$$

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

в) $$2x^2 + 5x + 2 = 0$$

$$D = 5^2 - 4 \cdot 2 \cdot 2 = 25 - 16 = 9$$

$$x_{1,2} = \frac{-5 \pm \sqrt{9}}{2 \cdot 2} = \frac{-5 \pm 3}{4}$$

$$x_1 = \frac{-5 + 3}{4} = \frac{-2}{4} = -\frac{1}{2}, x_2 = \frac{-5 - 3}{4} = \frac{-8}{4} = -2$$

г) $$3x^2 + 11x + 6 = 0$$

$$D = 11^2 - 4 \cdot 3 \cdot 6 = 121 - 72 = 49$$

$$x_{1,2} = \frac{-11 \pm \sqrt{49}}{2 \cdot 3} = \frac{-11 \pm 7}{6}$$

$$x_1 = \frac{-11 + 7}{6} = \frac{-4}{6} = -\frac{2}{3}, x_2 = \frac{-11 - 7}{6} = \frac{-18}{6} = -3$$

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