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МатематикаРешебник по алгебре 9 класс Макарычев Задание 522
Задание 522
\[\boxed{\text{522}\text{\ (522)}\text{.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\textbf{а)}\ x² - y^{2} = 5 \Longrightarrow\]
\[\Longrightarrow (x - y)(x + y) = 5;\]
\[1)\ \left\{ \begin{matrix} x - y = 1 \\ x + y = 5 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x = y + 1 \\ 2y = 4\ \ \ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} y = 2 \\ x = 3 \\ \end{matrix}; \right.\ \]
\[2)\ \left\{ \begin{matrix} x - y = 5 \\ x + y = 1 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x = y + 5 \\ 2y = - 4\ \ \ \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} y = - 2 \\ x = 3\ \ \ \ \\ \end{matrix}; \right.\ \]
\[3)\ \left\{ \begin{matrix} x - y = - 1 \\ x + y = - 5 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x = y - 1 \\ 2y = - 4\ \ \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} y = - 2 \\ x = - 3 \\ \end{matrix}; \right.\ \]
\[4)\ \left\{ \begin{matrix} x - y = - 5 \\ x + y = - 1 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x = y - 5 \\ 2y = 4\ \ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} y = 2\ \ \ \\ x = - 3. \\ \end{matrix} \right.\ \]
\[\textbf{б)}\ x² - y^{2} = 8 \Longrightarrow\]
\[\Longrightarrow (x - y)(x + y) = 8;\]
\[1)\ \left\{ \begin{matrix} x - y = 4 \\ x + y = 2 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x = y + 4 \\ 2y = - 2\ \ \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} y = - 1 \\ x = 3\ \ \ \\ \end{matrix} \right.\ ;\]
\[2)\ \left\{ \begin{matrix} x - y = 2 \\ x + y = 4 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x = y + 2 \\ 2y = 2\ \ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} y = 1 \\ x = 3 \\ \end{matrix} \right.\ ;\]
\[3)\ \left\{ \begin{matrix} x - y = - 4\ \ \\ x + y = - 2 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} x = y - 4 \\ 2y = 2\ \ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} y = 1\ \ \\ x = - 3 \\ \end{matrix} \right.\ ;\]
\[4)\ \left\{ \begin{matrix} x - y = - 2 \\ x + y = - 4\ \ \ \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} x = y - 2 \\ 2y = - 2\ \ \ \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} y = - 1 \\ x = - 3 \\ \end{matrix} \right.\ .\]
\[Ответ:а)\ (3;2);\ \ (3;\ - 2);\ \ \]
\[( - 3;\ - 2);\ \ ( - 3;2);\]
\[\textbf{б)}\ (3;\ - 1);(3;1);( - 3;1);\]
\[( - 3; - 1).\]
\[\boxed{\text{522.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]
\[\textbf{а)}\ \left\{ \begin{matrix} x² + y² \leq 25 \\ xy \leq 0\ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]
\[\textbf{б)}\ \left\{ \begin{matrix} x² + y² \geq 9 \\ xy \geq 0\ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]
