Решите систему уравнений: 2x^2+5xy+2y^2=0; x^2-xy-y^2=5.

\[x^{2} - x( - 2x) - ( - 2x)^{2} = 5\]

\[x^{2} + 2x^{2} - 4x^{2} = 5\]

\[- x^{2} = 5\]

\[x^{2} = - 5 \Longrightarrow \ нет\ решения.\]

\[( - 2y)^{2} - ( - 2y)y - y^{2} = 5\]

\[4y^{2} + 2y^{2} - y^{2} = 5\]

\[5y^{2} = 5\]

\[y^{2} = 1\]

\[y_{1} = - 1 \Longrightarrow \text{\ \ \ \ }x_{2} = - 2 \cdot 1 = - 2.\]

\[y_{2} = - 1 \Longrightarrow \text{\ \ \ \ }x_{2} = - 2 \cdot ( - 1) =\]

\[= 2.\]

\[Ответ:( - 2;1),\ (2;\ - 1).\]