Решите систему уравнений x-y=1; x^2+2y=33.

Ответ:

\[\left\{ \begin{matrix} x - y = 1\ \ \ \ \ \ \ \\ x^{2} + 2y = 33 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} y = x - 1\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x^{2} + 2 \cdot (x - 1) = 33 \\ \end{matrix} \right.\ \]

\[x^{2} + 2x - 2 - 33 = 0\]

\[x^{2} + 2x - 35 = 0\]

\[x_{1} + x_{2} = - 2;\ \ \ x_{1} \cdot x_{2} = - 35\]

\[x_{1} = - 7;\ \ \ \ x_{2} = 5\]

\[\left\{ \begin{matrix} x = - 7\ \ \ \ \ \ \ \ \\ y = - 7 - 1 \\ \end{matrix} \right.\ \Leftrightarrow \left\{ \begin{matrix} x = 5\ \ \ \ \ \ \ \ \\ y = 5 - 1 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} x = - 7 \\ y = - 8 \\ \end{matrix} \right.\ \Leftrightarrow \left\{ \begin{matrix} x = 5 \\ y = 4 \\ \end{matrix} \right.\ \]

\[Ответ:( - 7; - 8)\ или\ (5;4).\]