4. Решите уравнение и сделайте проверку: a) 9y2-4=0; б) -y² +5=0; в) 1-4у² = 0; г) 8у² + у = 0; д) бу-у² = 0; e) 0,1y2-0,5y = 0.

4. Решение уравнений и проверка:

а) $$9y^2 - 4 = 0$$

• $$9y^2 = 4$$
• $$y^2 = \frac{4}{9}$$
• $$y = \pm \frac{2}{3}$$

Проверка:

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

Ответ: $$y = \frac{2}{3}$$ и $$y = -\frac{2}{3}$$

б) $$-y^2 + 5 = 0$$

• $$y^2 = 5$$
• $$y = \pm \sqrt{5}$$

Проверка:

• $$-(\sqrt{5})^2 + 5 = -5 + 5 = 0$$
• $$-(-\sqrt{5})^2 + 5 = -5 + 5 = 0$$

Ответ: $$y = \sqrt{5}$$ и $$y = -\sqrt{5}$$

в) $$1 - 4y^2 = 0$$

• $$4y^2 = 1$$
• $$y^2 = \frac{1}{4}$$
• $$y = \pm \frac{1}{2}$$

Проверка:

• $$1 - 4(\frac{1}{2})^2 = 1 - 4 \cdot \frac{1}{4} = 1 - 1 = 0$$
• $$1 - 4(-\frac{1}{2})^2 = 1 - 4 \cdot \frac{1}{4} = 1 - 1 = 0$$

Ответ: $$y = \frac{1}{2}$$ и $$y = -\frac{1}{2}$$

г) $$8y^2 + y = 0$$

• $$y(8y + 1) = 0$$
• $$y = 0$$ или $$8y + 1 = 0$$
• $$y = 0$$ или $$y = -\frac{1}{8}$$

Проверка:

• $$8(0)^2 + 0 = 0$$
• $$8(-\frac{1}{8})^2 + (-\frac{1}{8}) = 8 \cdot \frac{1}{64} - \frac{1}{8} = \frac{1}{8} - \frac{1}{8} = 0$$

Ответ: $$y = 0$$ и $$y = -\frac{1}{8}$$

д) $$6y - y^2 = 0$$

• $$y(6 - y) = 0$$
• $$y = 0$$ или $$6 - y = 0$$
• $$y = 0$$ или $$y = 6$$

Проверка:

• $$6(0) - (0)^2 = 0$$
• $$6(6) - (6)^2 = 36 - 36 = 0$$

Ответ: $$y = 0$$ и $$y = 6$$

е) $$0.1y^2 - 0.5y = 0$$

• $$0.1y(y - 5) = 0$$
• $$0.1y = 0$$ или $$y - 5 = 0$$
• $$y = 0$$ или $$y = 5$$

Проверка:

• $$0.1(0)^2 - 0.5(0) = 0$$
• $$0.1(5)^2 - 0.5(5) = 0.1 \cdot 25 - 2.5 = 2.5 - 2.5 = 0$$

Ответ: $$y = 0$$ и $$y = 5$$