Решите систему уравнений y-x=2; y^2+4x=13.

Ответ:

\[\left\{ \begin{matrix} y - x = 2\ \ \ \ \ \ \ \\ y^{2} + 4x = 13 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} y = 2 + x\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ (2 + x)^{2} + 4x = 13 \\ \end{matrix} \right.\ \]

\[4 + 4x + x^{2} + 4x - 13 = 0\]

\[x^{2} + 8x - 9 = 0\]

\[x_{1} + x_{2} = - 8;\ \ \ x_{1} \cdot x_{2} = - 9\]

\[x_{1} = - 9;\ \ \ \ x_{2} = 1\]

\[\left\{ \begin{matrix} x = - 9\ \ \ \ \ \\ y = 2 - 9 \\ \end{matrix} \right.\ \Leftrightarrow \left\{ \begin{matrix} x = 1\ \ \ \ \ \ \ \ \\ y = 2 + 1 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} x = - 9 \\ y = - 7 \\ \end{matrix} \right.\ \Leftrightarrow \left\{ \begin{matrix} x = 1 \\ y = 3 \\ \end{matrix} \right.\ \]

\[Ответ:( - 9; - 7)\ или\ (1;3).\]