Решите систему уравнений: x^2-6y^2=-5; x^2+6y^2=7.

Ответ:

\[\left\{ \begin{matrix} x^{2} - 6y^{2} = - 5 \\ x^{2} + 6y^{2} = 7\ \ \ \\ \end{matrix}\text{\ \ \ }( + ) \right.\ \text{\ \ \ \ }\]

\[\left\{ \begin{matrix} 2x^{2} = 2\ \ \ \ \ \ \ \ \ \ \\ x^{2} + 6y^{2} = 7 \\ \end{matrix}\text{\ \ \ \ \ \ \ \ } \right.\ \]

\[\left\{ \begin{matrix} x^{2} = 1\ \ \ \ \ \ \ \ \ \ \ \ \ \\ x^{2} + 6y^{2} = 7 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} x^{2} = 1\ \ \\ 6y^{2} = 6 \\ \end{matrix}\text{\ \ \ \ \ \ \ } \right.\ \]

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

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

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

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

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

\[Ответ:(1;1),\ (1;\ - 1),\ \]

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