Решите систему уравнений: (2x+y)/(x-2y)+(2*(x-2y))/(2x+y)=3; x^2+3xy-y^2=25.

Ответ:

\[\left\{ \begin{matrix} \frac{2x + y}{x - 2y} + \frac{2 \cdot (x - 2y)}{2x + y} = 3 \\ x² + 3xy - y^{2} = 25\ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[Пусть\ \ \frac{2x + y}{x - 2y} = t:\]

\[t + \frac{2}{t} - 3 = 0\ \ \ | \cdot t\]

\[t^{2} - 3t + 2 = 0\]

\[t_{1} + t_{2} = 3,\ \ \ t_{1} \cdot t_{2} = 2\]

\[t_{1} = 2,\ \ t_{2} = 1\]

\[Ответ:(5;0);\ \ ( - 5;0).\]