Решебник по алгебре 9 класс Мерзляк Задание 469

\[\boxed{\text{469\ (469).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\left\{ \begin{matrix} x^{2} + 10xy + 25y^{2} = 49 \\ x - 5y = - 3\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]

\[\text{\ \ }\left\{ \begin{matrix} (x + 5y)^{2} = 49 \\ x = 5y - 3\ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ }\]

\[\left\{ \begin{matrix} x + 5y = 7 \\ x = 5y - 3 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ }или\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \]

\[\text{\ \ }\left\{ \begin{matrix} x + 5y = - 7 \\ x = 5y - 3\ \ \ \\ \end{matrix} \right.\ \]

\[Ответ:(2;1);( - 5;\ - 0,4).\]

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

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

\[\left\{ \begin{matrix} 4x + 2y = 16 \\ x = 4 - 2y\ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} 4(4 - 2y) + 2y - 16 = 0 \\ x = 4 - 2y\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[16 - 8y + 2y - 16 = 0\]

\[- 6y = 0\]

\[\left\{ \begin{matrix} y = 0 \\ x = 4 \\ \end{matrix} \right.\ \]

\[Ответ:(4;0).\]

\[3)\ \left\{ \begin{matrix} x^{2} + y^{2} = 10 \\ xy = 3\ \ \ \ \ | \cdot 2 \\ \end{matrix} \right.\ \ \ \ + \ \ \]

\[+ \left\{ \begin{matrix} x^{2} + y^{2} + 2xy = 16 \\ xy = 3\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]

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

\[\left\{ \begin{matrix} x + y = 4 \\ xy = 3\ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ }или\ \text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ }\]

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