Решебник по алгебре 9 класс Макарычев Задание 391

 

\[\boxed{\text{391\ (391).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\textbf{а)}\ y = \frac{4}{\sqrt{(3x - 1)(6x + 1)}}\]

\[(3x - 1)(6x + 1) > 0\]

\[6 \cdot \left( x + \frac{1}{6} \right)\left( x - \frac{1}{3} \right) > 0\]

\[x \in \left( - \infty; - \frac{1}{6} \right) \cup \left( \frac{1}{3}; + \infty \right).\]

\[\textbf{б)}\ y = \frac{7}{\sqrt{(11x + 2)(x - 4)}}\]

\[(11x + 2)(x - 4) > 0\]

\[11 \cdot \left( x + \frac{2}{11} \right)(x - 4) > 0\]

\[x \in \left( - \infty; - \frac{2}{11} \right) \cup (4; + \infty)\text{.\ }\]

\[\boxed{\text{391.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]

\[\textbf{а)}\ \left\{ \begin{matrix} x^{2} + y^{2} = 12 \\ xy = - 6\ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} x = - \frac{6}{y}\text{\ \ \ \ \ \ \ \ \ \ \ } \\ \frac{36}{y^{2}} + y^{2} = 12 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} x = - \frac{6}{y}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \\ 36 + y^{4} - 12y^{2} = 0 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} x = - \frac{6}{y}\text{\ \ \ \ \ \ \ \ \ \ \ \ } \\ \left( y^{2} - 6 \right)^{2} = 0 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} y_{1} = \sqrt{6}\text{\ \ \ \ } \\ x_{1} = - \sqrt{6} \\ \end{matrix} \right.\ \text{\ \ \ \ }или\ \ \ \]

\[\left\{ \begin{matrix} y_{2} = - \sqrt{6} \\ x_{2} = \sqrt{6.}\text{\ \ \ } \\ \end{matrix} \right.\ \]

\[\textbf{б)}\ \left\{ \begin{matrix} 2x^{2} - y^{2} = 34 \\ xy = 20\ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} x = \frac{20}{y}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \\ 2 \cdot \frac{400}{y^{2}} - y^{2} = 34 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} x = \frac{20}{y}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \\ 800 - y^{4} - 34y^{2} = 0 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} x = \frac{20}{y}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \\ y^{4} + 34y^{2} - 800 = 0 \\ \end{matrix} \right.\ \]

\[Пусть\ t = y^{2};\ \ t \geq 0:\]

\[t^{2} + 34t - 800 = 0\]

\[D = 17^{2} + 800 = 1089\]

\[t_{1,2} = - 17 \pm 33\]

\[так\ как\ t \geq 0:\]

\[t = 16 \Longrightarrow y^{2} = 16.\]

\[1)\ y_{1} = 4;\ \ x_{1} = 5;\]

\[2)y_{2} = - 4;\ \ x_{2} = - 5.\]

\[Ответ:а)\ \left( - \sqrt{6};\sqrt{6} \right);\ \]

\[\ \left( \sqrt{6};\ - \sqrt{6} \right);\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ б)\ (5;4);\ \ ( - 5;\ - 4).\]