Решите систему уравнений: 2x^2-y^2=41; 2x^2+y^2=59.

\[\left\{ \begin{matrix} 2x^{2} - y^{2} = 41 \\ 2x^{2} + y^{2} = 59 \\ \end{matrix} \right.\ \ ( + )\]

\[4x^{2} = 100\]

\[x^{2} = 25\]

\[x = \pm 5.\]

\[y^{2} = 59 - 2x^{2}\]

\[y = \sqrt{59 - 2x^{2}} =\]

\[= \sqrt{59 - 2 \cdot 25} = \sqrt{9} = \pm 3.\]

\[Ответ:(5;3);(5;\ - 3);( - 5;3);\]

\[( - 5;\ - 3).\]