Решебник по алгебре 8 класс Мерзляк Задание 685

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\[1)\ \left| x^{2} + 10x - 4 \right| = 20\]

\[\left\{ \begin{matrix} x = - 15 \\ x = 3\ \ \ \ \ \\ x \geq 0\ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[Ответ:3.\]

\[3)\frac{x^{3}}{|x|} - 14x - 15 = 0\]

\[\left\{ \begin{matrix} x^{2} - 14x - 15 = 0 \\ x > 0 \\ \end{matrix} \right.\ \]

\[D = 196 + 4 \cdot 15 = 256\]

\[x = \frac{14 \pm 16}{2}\]

\[\left\{ \begin{matrix} x = 15 \\ x = - 1 \\ x > 0 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} - x^{2} - 14x - 15 = 0 \\ x < 0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[D = 196 - 4 \cdot 15 = 136\]

\[x = \frac{14 \pm \sqrt{136}}{- 2} = \frac{7 \pm \sqrt{34}}{- 1} =\]

\[= - 7 \pm \sqrt{34}\]

\[\left\{ \begin{matrix} x = - 7 - \sqrt{34} \\ x = - 7 + \sqrt{34} \\ x < 0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[Ответ:15;\ - 7 - \sqrt{34};\ - 7 + \sqrt{34}.\]

\[4)\ x² - 8\sqrt{x^{2}} - 9 = 0\]

\[x^{2} - 8|x| - 9 = 0\]