\[\left\{ \begin{matrix} 2x^{2} - y^{2} = 41 \\ 2x^{2} + y^{2} = 59 \\ \end{matrix} \right.\ \ ( + )\]
\[4x^{2} = 100\]
\[x^{2} = 25\]
\[x = \pm 5.\]
\[y^{2} = 59 - 2x^{2}\]
\[y = \sqrt{59 - 2x^{2}} =\]
\[= \sqrt{59 - 2 \cdot 25} = \sqrt{9} = \pm 3.\]
\[Ответ:(5;3);(5;\ - 3);( - 5;3);\]
\[( - 5;\ - 3).\]