Решите систему уравнений x-y=3; x^2-xy-2y^2=7.

Ответ:

\[\left\{ \begin{matrix} x - y = 3\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x^{2} - xy - 2y^{2} = 7 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} x = 3 + y\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ (3 + y)^{2} - y(3 + y) - 2y^{2} = 7 \\ \end{matrix} \right.\ \]

\[9 + 6y + y^{2} - 3y - y^{2} - 2y^{2} - 7 = 0\]

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

\[D = 9 + 16 = 25\]

\[y = \frac{- 3 - 5}{- 4} = 2;\ \]

\[y = \frac{- 3 + 5}{- 4} = - \frac{1}{2}\]

\[\left\{ \begin{matrix} x = 5 \\ y = 2 \\ \end{matrix} \right.\ \ или\ \left\{ \begin{matrix} x = 2,5\ \ \ \\ y = - 0,5 \\ \end{matrix} \right.\ \]

\[Ответ:(5;2);\ \ (2,5;\ - 0,5).\]