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

Ответ:

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

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

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

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

\[D_{1} = 1 + 35 = 36\]

\[x_{1} = - 1 + 6 = 5;\]

\[x_{2} = - 1 - 6 = - 7;\]

\[y_{1} = 5 - 1 = 4;\]

\[y_{2} = - 7 - 1 = - 8.\]

\[Ответ:(5;4);\ \ ( - 7; - 8).\]