Решите систему уравнений: x-5y=2; x^2-y=10.

Ответ:

\[\left\{ \begin{matrix} x - 5y = 2\ \ \\ x^{2} - y = 10 \\ \end{matrix} \right.\ \text{\ \ \ \ }\left\{ \begin{matrix} x = 2 + 5y\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ (2 + 5y)^{2} - y = 10 \\ \end{matrix} \right.\ \]

\[4 + 20y + 25y^{2} - y - 10 = 0\]

\[25y^{2} + 19y - 6 = 0\]

\[D = 361 + 600 = 961 = 31^{2}\]

\[y_{1} = \frac{- 19 + 31}{50} = \frac{12}{50} = \frac{6}{25};\]

\[y_{2} = \frac{- 19 - 31}{50} = - \frac{50}{50} = - 1.\ \]

\[\left\{ \begin{matrix} y = - 1\ \ \ \ \\ x = 2 - 5 \\ \end{matrix} \right.\ \ \ \ \ или\ \ \ \left\{ \begin{matrix} y = \frac{6}{25}\text{\ \ \ \ \ } \\ x = 2 - \frac{6}{5} \\ \end{matrix} \right.\ \mathbf{\ }\]

\[\left\{ \begin{matrix} y = - 1 \\ x = - 3 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} y = 0,24 \\ x = 0,8\ \ \ \\ \end{matrix} \right.\ \ \]

\[Ответ:( - 3; - 1)\ и\ (0,8;0,24)\text{.\ }\]