Решебник по алгебре 9 класс Мерзляк Задание 757

\[\boxed{\mathbf{757\ (757).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\left\{ \begin{matrix} x^{2} - 3y^{2} = 46 \\ x + y = 6\ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} x = 6 - y\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ (6 - y)^{2} - 3y^{2} = 46 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\text{\ \ \ \ }\left\{ \begin{matrix} x = 6 - y\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 36 - 12y + y^{2} - 3y^{2} = 46 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} - 2y^{2} - 12y - 10 = 0\ \ \ \ |\ :( - 2) \\ x = 6 - y\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} y^{2} + 6y + 5 = 0 \\ x = 6 - y\ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[y_{1} + y_{2} = - 6,\ \ y_{1}y_{2} = 5\]

\[\left\{ \begin{matrix} y = - 5\ \ \ \ \\ x = 6 + 5 \\ \end{matrix} \right.\ \text{\ \ \ \ \ }или\ \ \ \ \ \ \ \left\{ \begin{matrix} y = - 1\ \ \ \\ x = 6 + 1 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} y = - 5 \\ x = 11 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} y = - 1 \\ x = 7\ \ \ \ \\ \end{matrix} \right.\ \]

\[Ответ:(11;\ - 5);\ \ (7;\ - 1).\]

\[2)\ \left\{ \begin{matrix} x^{2} - 2y^{2} = - 4 \\ x^{2} + 2y^{2} = 12 \\ \end{matrix} \right.\ + \ \ \ \ \]

\[\left\{ \begin{matrix} 2x^{2} = 8\ \ \ \ \ \ \ \ \ \ \ \ \\ x^{2} + 2y^{2} = 12 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

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

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

\[Ответ:(2;2),\ (2;\ - 2),\ \]

\[( - 2;2),\ ( - 2;\ - 2)\text{.\ }\]