Решите систему уравнений 3x+y=10; x^2-y=8.

Ответ:

\[\left\{ \begin{matrix} 3x + y = 10 \\ x^{2} - y = 8\ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} y = 10 - 3x\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x^{2} - 10 + 3x - 8 = 0 \\ \end{matrix} \right.\ \]

\[x^{2} + 3x - 18 = 0\]

\[D = 9 + 72 = 81\]

\[x_{1} = \frac{- 3 + 9}{2} = 3;\ \ \ x_{2} = \frac{- 3 - 9}{2} = - 6.\]

\[\left\{ \begin{matrix} x = 3 \\ y = 1 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\left\{ \begin{matrix} x = - 6 \\ y = 28\ \\ \end{matrix} \right.\ \ \]

\[Ответ:(3;1);( - 6;28).\]