6. Решите уравнение: a) (x + 0,1)(x – 1/6)(x + 3,9) = 0; б) 5x(4x – 0,2) = 0; в) 6,3x – 0,7x² = 0; г) 1/5 u² – 9/20 = 0; д) 1,4a² – 4,2 = 0; e) 8y + 0,4y² = 0.

6. Решите уравнение:

a) $$(x + 0.1)(x - \frac{1}{6})(x + 3.9) = 0$$

$$x + 0.1 = 0$$ или $$x - \frac{1}{6} = 0$$ или $$x + 3.9 = 0$$

$$x_1 = -0.1$$, $$x_2 = \frac{1}{6}$$, $$x_3 = -3.9$$

Ответ: x = -0.1, x = 1/6, x = -3.9

б) $$5x(4x - 0.2) = 0$$

$$5x = 0$$ или $$4x - 0.2 = 0$$

$$x_1 = 0$$, $$4x = 0.2$$, $$x_2 = \frac{0.2}{4} = 0.05$$

Ответ: x = 0, x = 0.05

в) $$6.3x - 0.7x^2 = 0$$

$$x(6.3 - 0.7x) = 0$$

$$x_1 = 0$$ или $$6.3 - 0.7x = 0$$

$$0.7x = 6.3$$

$$x_2 = \frac{6.3}{0.7} = 9$$

Ответ: x = 0, x = 9

г) $$\frac{1}{5}u^2 - \frac{9}{20} = 0$$

$$\frac{1}{5}u^2 = \frac{9}{20}$$

$$u^2 = \frac{9}{20} \cdot 5 = \frac{9}{4}$$

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

Ответ: u = 3/2, u = -3/2

д) $$1.4a^2 - 4.2 = 0$$

$$1.4a^2 = 4.2$$

$$a^2 = \frac{4.2}{1.4} = 3$$

$$a = \pm\sqrt{3}$$

Ответ: a = $$\sqrt{3}$$, a = $$\sqrt{3}$$

e) $$8y + 0.4y^2 = 0$$

$$y(8 + 0.4y) = 0$$

$$y_1 = 0$$ или $$8 + 0.4y = 0$$

$$0.4y = -8$$

$$y_2 = -\frac{8}{0.4} = -20$$

Ответ: y = 0, y = -20