№5 Решите уравнение: 1) x² - 2 x = 0; 4) 10z2 + 7z = 0; 2) y² - 4y = 0; 5) x(3x - 5) – 4(3x - 5) = 0; 8) 5y2 - y = 0; 6) 2y(9y - 6) + 5(6-9y) = 0.

Решим уравнения:

1. $$x^2 - x = 0$$

   $$x(x-1) = 0$$

   $$x_1 = 0, x_2 = 1$$

2. $$y^2 - 4y = 0$$

   $$y(y-4) = 0$$

   $$y_1 = 0, y_2 = 4$$

3. $$5y^2 - y = 0$$

   $$y(5y - 1) = 0$$

   $$y_1 = 0, y_2 = \frac{1}{5}$$

4. $$10z^2 + 7z = 0$$

   $$z(10z + 7) = 0$$

   $$z_1 = 0, z_2 = -\frac{7}{10}$$

5. $$x(3x-5) - 4(3x-5) = 0$$

   $$(3x-5)(x-4) = 0$$

   $$x_1 = \frac{5}{3}, x_2 = 4$$

6. $$2y(9y-6) + 5(6-9y) = 0$$

   $$18y^2 - 12y + 30 - 45y = 0$$

   $$18y^2 - 57y + 30 = 0$$

   $$6y^2 - 19y + 10 = 0$$

   $$D = (-19)^2 - 4 \cdot 6 \cdot 10 = 361 - 240 = 121$$

   $$y_1 = \frac{19 + 11}{12} = \frac{30}{12} = \frac{5}{2}$$, $$y_2 = \frac{19 - 11}{12} = \frac{8}{12} = \frac{2}{3}$$

Ответ: 1) $$x_1 = 0, x_2 = 1$$, 2) $$y_1 = 0, y_2 = 4$$, 3) $$y_1 = 0, y_2 = \frac{1}{5}$$, 4) $$z_1 = 0, z_2 = -\frac{7}{10}$$, 5) $$x_1 = \frac{5}{3}, x_2 = 4$$, 6) $$y_1 = \frac{5}{2}$$, $$y_2 = \frac{2}{3}$$