Решите систему уравнений: xy+x^2=4; y=x+2.

Ответ:

\[x^{2} + 2x + x^{2} - 4 = 0\]

\[2x^{2} + 2x - 4 = 0\ \ \ \ \ |\ :2\]

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

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

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

\[\left\{ \begin{matrix} x = - 2 \\ y = 0\ \ \ \ \\ \end{matrix} \right.\ \ \ \ \ или\ \ \ \left\{ \begin{matrix} x = 1 \\ y = 3 \\ \end{matrix} \right.\ \]

\[Ответ:( - 2;0);\ \ (1;3).\]