Решебник по алгебре 8 класс Мерзляк Задание 776

\[\boxed{\mathbf{776\ (776).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\text{\ x}^{4} - 29x^{2} + 100 = 0\]

\(\left\{ \begin{matrix} x^{2} = t\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ t² - 29t + 100 = 0 \\ \end{matrix} \right.\ \)

\(t_{1} + t_{2} = 29,\ \ t_{1} \cdot t_{2} = 100,\)

\[\text{\ \ }t_{1} = 25,\ \ t_{2} = 4\]

\[Ответ:\ x = \pm 5;x = \pm 2.\ \]

\[2)\ \text{\ x}^{4} - 9x^{2} + 20 = 0\]

\(\left\{ \begin{matrix} x^{2} = t\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ t² - 9t + 20 = 0 \\ \end{matrix} \right.\ \)

\(t_{1} + t_{2} = 9,\ \ t_{1} \cdot t_{2} = 20,\ \ \)

\[t_{1} = 5,\ \ t_{2} = 4\]

\[Ответ:\ x = \pm \sqrt{5};x = \ \pm 2.\]

\[3)\text{\ x}^{4} - 2x^{2} - 24 = 0\]

\(\left\{ \begin{matrix} x^{2} = t\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ t² - 2t - 24 = 0 \\ \end{matrix} \right.\ \)

\[t_{1} + t_{2} = 2,\ \ t_{1} \cdot t_{2} = - 24,\ \]

\[\ t_{1} = 6,\ \ t_{2} = - 4\]

\[Ответ:\ x = \pm \sqrt{6}.\]

\[4)\ \text{\ x}^{4} + 3x^{2} - 70 = 0\]

\(\left\{ \begin{matrix} x^{2} = t\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ t² + 3t - 70 = 0 \\ \end{matrix} \right.\ \)

\(t_{1} + t_{2} = - 3,\ \ t_{1} \cdot t_{2} = - 70,\ \ \)

\[t_{1} = - 10,\ \ t_{2} = 7\]

\[Ответ:\ x = \pm \sqrt{7}.\]

\[5)\ {\ 9x}^{4} - 10x^{2} + 1 = 0\]

\(\left\{ \begin{matrix} x^{2} = t\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 9t² - 10t + 1 = 0 \\ \end{matrix} \right.\ \)

\[D = 100 - 36 = 64,\ \ \]

\[t_{1} = \frac{10 + 8}{18} = 1,\ \ \]

\[t_{2} = \frac{10 - 8}{18} = \frac{1}{9}\]

\[Ответ:x = \pm 1;x = \pm \frac{1}{3}.\]

\[6){\ 2x}^{4} - 5x^{2} + 2 = 0\]

\(\left\{ \begin{matrix} x^{2} = t\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 2t² - 5t + 2 = 0 \\ \end{matrix} \right.\ \)

\[D = 25 - 16 = 9,\]

\[\text{\ \ }t_{1} = \frac{5 - 3}{4} = \frac{1}{2},\ \ \]

\[t_{2} = \frac{5 + 3}{4} = 2\]

\[Ответ:x = \pm \frac{1}{\sqrt{2}};\ x = \pm \sqrt{2}\text{.\ }\]