ГДЗ по алгебре 9 класс Макарычев Задание 515

\[\boxed{\text{515\ (515).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\textbf{а)}\ \left\{ \begin{matrix} 4x(x + y) + y^{2} = 49 \\ 4x(x - y) + y^{2} = 81 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} 4x^{2} + 4xy + y^{2} = 49 \\ 4x^{2} - 4xy + y^{2} = 81 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} (2x + y)^{2} = 49 \\ (2x - y)^{2} = 81 \\ \end{matrix} \right.\ \]

\[1)\ \left\{ \begin{matrix} 2x + y = 7 \\ 2x - y = 9 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x = 4\ \ \ \ \\ y = - 1 \\ \end{matrix} \right.\ ;\]

\[2)\left\{ \begin{matrix} 2x + y = 7\ \ \\ 2x - y = - 9 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x = - 0,5 \\ y = 8\ \ \ \ \ \\ \end{matrix}; \right.\ \]

\(3)\ \left\{ \begin{matrix} 2x + y = - 7 \\ 2x - y = 9\ \ \ \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x = 0,5 \\ y = - 8 \\ \end{matrix} \right.\ ;\ \)

\[4)\ \left\{ \begin{matrix} 2x + y = - 7 \\ 2x - y = - 9 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x = - 4 \\ y = 1.\ \ \\ \end{matrix} \right.\ \]

\[\textbf{б)}\ \left\{ \begin{matrix} 3x(3x - y) + 4y^{2} = 64\ \\ 3x(3x + 4y) + 4y^{2} = 16 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} 9x^{2} - 12xy + 4y^{2} = 64 \\ 9x^{2} + 12xy + 4y^{2} = 16 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} (3x - 2y)^{2} = 64 \\ (3x + 2y)^{2} = 16 \\ \end{matrix} \right.\ \]

\[1)\ \left\{ \begin{matrix} 3x - 2y = 8 \\ 3x + 2y = 4 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x = 2\ \ \ \\ y = - 1 \\ \end{matrix} \right.\ ;\]

\[2)\ \left\{ \begin{matrix} 3x - 2y = 8\ \ \\ 3x + 2y = - 4 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x = \frac{2}{3}\text{\ \ } \\ y = - 3 \\ \end{matrix} \right.\ ;\]

\[3)\ \left\{ \begin{matrix} 3x - 2y = - 8 \\ 3x + 2y = 4\ \ \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x = - \frac{2}{3} \\ y = 3\ \ \ \\ \end{matrix} \right.\ ;\]

\[4)\ \left\{ \begin{matrix} 3x - 2y = - 8 \\ 3x + 2y = - 4 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x = - 2 \\ y = 1.\ \ \ \\ \end{matrix} \right.\ \]

\[Ответ:а)\ (4;\ - 1);\ \ ( - 4;1);\ \ \]

\[(0,5;\ - 8);( - 0,5;8);\]

\[\textbf{б)}\ (2;\ - 1);( - 2;1);\left( \frac{2}{3};\ - 3 \right);\]

\[\left( - \frac{2}{3};3 \right).\]