4. Решите уравнение и сделайте проверку: a) 25y² – 1 = 0; б) –y² + 2 = 0; в) 9 – 16y² = 0; г) 7y² + y = 0; д) 4y – y² = 0; e) 0,2y² – y = 0.

Решим уравнения и сделаем проверку:

a) $$25y^2 - 1 = 0$$

$$25y^2 = 1$$

$$y^2 = \frac{1}{25}$$

$$y = \pm\sqrt{\frac{1}{25}}$$

$$y = \pm\frac{1}{5}$$

Проверка:

$$25(\frac{1}{5})^2 - 1 = 25 \cdot \frac{1}{25} - 1 = 1 - 1 = 0$$

$$25(-\frac{1}{5})^2 - 1 = 25 \cdot \frac{1}{25} - 1 = 1 - 1 = 0$$

Ответ: y = 1/5, y = -1/5

б) $$-y^2 + 2 = 0$$

$$y^2 = 2$$

$$y = \pm\sqrt{2}$$

Проверка:

$$-(\sqrt{2})^2 + 2 = -2 + 2 = 0$$

$$-(-\sqrt{2})^2 + 2 = -2 + 2 = 0$$

Ответ: y =$$\sqrt{2}$$, y = $$\sqrt{2}$$

в) $$9 - 16y^2 = 0$$

$$16y^2 = 9$$

$$y^2 = \frac{9}{16}$$

$$y = \pm\sqrt{\frac{9}{16}}$$

$$y = \pm\frac{3}{4}$$

Проверка:

$$9 - 16(\frac{3}{4})^2 = 9 - 16 \cdot \frac{9}{16} = 9 - 9 = 0$$

$$9 - 16(-\frac{3}{4})^2 = 9 - 16 \cdot \frac{9}{16} = 9 - 9 = 0$$

Ответ: y = 3/4, y = -3/4

г) $$7y^2 + y = 0$$

$$y(7y + 1) = 0$$

$$y_1 = 0$$

$$7y + 1 = 0$$

$$7y = -1$$

$$y_2 = -\frac{1}{7}$$

Проверка:

$$7(0)^2 + 0 = 0$$

$$7(-\frac{1}{7})^2 + (-\frac{1}{7}) = 7\cdot\frac{1}{49} - \frac{1}{7} = \frac{1}{7} - \frac{1}{7} = 0$$

Ответ: y = 0, y = -1/7

д) $$4y - y^2 = 0$$

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

$$y_1 = 0$$

$$4 - y = 0$$

$$y_2 = 4$$

Проверка:

$$4(0) - (0)^2 = 0$$

$$4(4) - (4)^2 = 16 - 16 = 0$$

Ответ: y = 0, y = 4

e) $$0.2y^2 - y = 0$$

$$y(0.2y - 1) = 0$$

$$y_1 = 0$$

$$0.2y - 1 = 0$$

$$0.2y = 1$$

$$y_2 = \frac{1}{0.2} = 5$$

Проверка:

$$0.2(0)^2 - 0 = 0$$

$$0.2(5)^2 - 5 = 0.2 \cdot 25 - 5 = 5 - 5 = 0$$

Ответ: y = 0, y = 5