Решебник по алгебре 8 класс Мерзляк ФГОС Задание 634

\[\boxed{\mathbf{634\ (634).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ \frac{x^{2} + x}{7} - \frac{x}{3} = 0\]

\[\frac{3x^{2} + 3x - 7x}{21} = 0\ \ | \cdot 21\]

\[3x^{2} - 4x = 0\]

\[x(3x - 4) = 0\]

\[x = 0,\ \ 3x = 4\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = \frac{4}{3} = 1\frac{1}{3}\]

\[Ответ:x = 0;\ \ x = 1\frac{1}{3}.\]

\[2)\ \frac{x^{2} + 1}{6} - \frac{x^{2} + 2}{4} = - 1\]

\[\frac{4x^{2} + 4 - 6x^{2} - 12}{24} = - 1\ \ \ | \cdot 24\]

\[- 2x^{2} - 8 = - 24\]

\[- 2x^{2} = - 16\]

\[x^{2} = 8\]

\[x = \sqrt{8} = 2\sqrt{2}\]

\[x = - \sqrt{8} = - 2\sqrt{2}\]

\[Ответ:\ x = - 2\sqrt{2};x = 2\sqrt{2}.\]

\[\boxed{\mathbf{6}\mathbf{34}\mathbf{\text{.\ }}Еуроки\ - \ ДЗ\ без\ мороки}\]

\[\sqrt{x} = - x^{2}\]

\[\left\{ \begin{matrix} x = x^{4} \\ x \geq 0 \\ x \leq 0 \\ \end{matrix} \right.\ \]

\[x - x^{4} = 0\]

\[x\left( 1 - x^{3} \right) = 0\]

\[\left\{ \begin{matrix} x = 1 \\ x = 0 \\ x = 0 \\ \end{matrix} \right.\ \]

\[Ответ:x = 0.\]