Решите систему уравнений x^2-5y=-11; x+y=-1.

Ответ:

\[\left\{ \begin{matrix} x^{2} - 5y = - 11 \\ x + y = - 1\ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} y = - 1 - x\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x^{2} - 5 \cdot ( - 1 - x) = - 11 \\ \end{matrix} \right.\ \]

\[x^{2} - 5 + 5x + 11 = 0\]

\[x^{2} + 5x + 6 = 0\]

\[x_{1} + x_{2} = - 5;\ \ \ x_{1} \cdot x_{2} = 6\]

\[x_{1} = - 3;\ \ \ x_{2} = - 2.\]

\[\left\{ \begin{matrix} x = - 3 \\ y = 2\ \ \ \\ \end{matrix} \right.\ \ \ \ \ или\ \ \ \left\{ \begin{matrix} x = - 2 \\ y = 1\ \ \ \\ \end{matrix} \right.\ \]

\[Ответ:( - 3;2);( - 2;1).\]