Решите систему уравнений: x+y=-5; xy=-14.

Ответ:

\[\left\{ \begin{matrix} x + y = - 5 \\ xy = - 14\ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} x = - 5 - y\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ ( - 5 - y) \cdot y = - 14 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} x = - 5 - y\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ - y^{2} - 5y + 14 = 0 \\ \end{matrix} \right.\ \]

\[y^{2} + 5y - 14 = 0\]

\[y_{1} + y_{2} = - 5,\ \ y_{1} \cdot y_{2} = - 14\]

\[y_{1} = - 7,\ \ y_{2} = 2\]

\[\left\{ \begin{matrix} x = 2\ \ \ \ \\ y = - 7 \\ \end{matrix} \right.\ \ \ \ \ \ или\ \ \ \ \left\{ \begin{matrix} x = - 7 \\ y = 2\ \ \ \\ \end{matrix} \right.\ \]

\[Ответ:(2;\ - 7);\ \ ( - 7;2).\]