Решебник по алгебре 9 класс Макарычев Задание 487

 

\[\boxed{\text{487\ (487).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\textbf{а)}\ y \leq x^{2} - 4\]

\(\ \)

\[\textbf{б)}\ y \geq (x - 2)^{2} - 1\]

\(\ \)

\[\textbf{в)}\ x^{2} + y^{2} \leq 25\]

\(\ \)

\[\textbf{г)}\ (x - 1)^{2} + (y - 2)^{2} \leq 4\]

\(\ \)

\[\boxed{\text{487.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]

\[\textbf{а)}\ x² - y^{2} = 5 \Longrightarrow\]

\[\Longrightarrow (x - y)(x + y) = 5;\]

\[1)\ \left\{ \begin{matrix} x - y = 1 \\ x + y = 5 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x = y + 1 \\ 2y = 4\ \ \ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} y = 2 \\ x = 3 \\ \end{matrix}; \right.\ \]

\[2)\ \left\{ \begin{matrix} x - y = 5 \\ x + y = 1 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x = y + 5 \\ 2y = - 4\ \ \ \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} y = - 2 \\ x = 3\ \ \ \ \\ \end{matrix}; \right.\ \]

\[3)\ \left\{ \begin{matrix} x - y = - 1 \\ x + y = - 5 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} x = y - 1 \\ 2y = - 4\ \ \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} y = - 2 \\ x = - 3 \\ \end{matrix}; \right.\ \]

\[4)\ \left\{ \begin{matrix} x - y = - 5 \\ x + y = - 1 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} x = y - 5 \\ 2y = 4\ \ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} y = 2\ \ \ \\ x = - 3. \\ \end{matrix} \right.\ \]

\[\textbf{б)}\ x² - y^{2} = 8 \Longrightarrow\]

\[\Longrightarrow (x - y)(x + y) = 8;\]

\[1)\ \left\{ \begin{matrix} x - y = 4 \\ x + y = 2 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x = y + 4 \\ 2y = - 2\ \ \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} y = - 1 \\ x = 3\ \ \ \\ \end{matrix} \right.\ ;\]

\[2)\ \left\{ \begin{matrix} x - y = 2 \\ x + y = 4 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x = y + 2 \\ 2y = 2\ \ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} y = 1 \\ x = 3 \\ \end{matrix} \right.\ ;\]

\[3)\ \left\{ \begin{matrix} x - y = - 4\ \ \\ x + y = - 2 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} x = y - 4 \\ 2y = 2\ \ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} y = 1\ \ \\ x = - 3 \\ \end{matrix} \right.\ ;\]

\[4)\ \left\{ \begin{matrix} x - y = - 2 \\ x + y = - 4\ \ \ \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} x = y - 2 \\ 2y = - 2\ \ \ \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} y = - 1 \\ x = - 3 \\ \end{matrix} \right.\ .\]

\[Ответ:а)\ (3;2);\ \ (3;\ - 2);\ \ \]

\[( - 3;\ - 2);\ \ ( - 3;2);\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ б)\ (3;\ - 1);(3;1);\]

\[( - 3;1);( - 3; - 1).\]