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

Решим уравнения и сделаем проверку:

a) $$9y^2 - 4 = 0$$

$$9y^2 = 4$$

$$y^2 = \frac{4}{9}$$

$$y = \pm \frac{2}{3}$$

Проверка:

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

б) $$-y^2 + 5 = 0$$

$$y^2 = 5$$

$$y = \pm \sqrt{5}$$

Проверка:

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

в) $$1 - 4y^2 = 0$$

$$4y^2 = 1$$

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

$$y = \pm \frac{1}{2}$$

Проверка:

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

г) $$8y^2 + y = 0$$

$$y(8y + 1) = 0$$

$$y = 0$$ или $$8y + 1 = 0 \Rightarrow y = -\frac{1}{8}$$

Проверка:

$$8(0)^2 + 0 = 0$$

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

д) $$6y - y^2 = 0$$

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

$$y = 0$$ или $$6 - y = 0 \Rightarrow y = 6$$

Проверка:

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

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

e) $$0.1y^2 - 0.5y = 0$$

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

$$y = 0$$ или $$y - 5 = 0 \Rightarrow y = 5$$

Проверка:

$$0.1(0)^2 - 0.5(0) = 0$$

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

Ответ: a) $$y = \pm \frac{2}{3}$$, б) $$y = \pm \sqrt{5}$$, в) $$y = \pm \frac{1}{2}$$, г) $$y = 0$$ или $$y = -\frac{1}{8}$$, д) $$y = 0$$ или $$y = 6$$, e) $$y = 0$$ или $$y = 5$$