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

1. а) $$25y^2 - 1 = 0$$ $$25y^2 = 1$$ $$y^2 = \frac{1}{25}$$ $$y = \pm \frac{1}{5}$$

Проверка:

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

2. б) $$-y^2 + 2 = 0$$ $$y^2 = 2$$ $$y = \pm \sqrt{2}$$

Проверка:

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

3. в) $$9 - 16y^2 = 0$$ $$16y^2 = 9$$ $$y^2 = \frac{9}{16}$$ $$y = \pm \frac{3}{4}$$

Проверка:

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

4. г) $$7y^2 + y = 0$$ $$y(7y + 1) = 0$$ $$y = 0$$ или $$7y + 1 = 0$$ $$y = -\frac{1}{7}$$

Проверка:

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

5. д) $$4y - y^2 = 0$$ $$y(4 - y) = 0$$ $$y = 0$$ или $$4 - y = 0$$ $$y = 4$$

Проверка:

$$4 \cdot 0 - 0^2 = 0$$ $$4 \cdot 4 - 4^2 = 16 - 16 = 0$$

6. е) $$0,2y^2 - y = 0$$ $$y(0,2y - 1) = 0$$ $$y = 0$$ или $$0,2y - 1 = 0$$ $$0,2y = 1$$ $$y = 5$$

Проверка:

$$0,2 \cdot 0^2 - 0 = 0$$ $$0,2 \cdot 5^2 - 5 = 0,2 \cdot 25 - 5 = 5 - 5 = 0$$

Ответ: а) y = ±1/5; б) y = ±√2; в) y = ±3/4; г) y = 0, y = -1/7; д) y = 0, y = 4; е) y = 0, y = 5