Решите систему уравнений: xy+y^2=24; x-2y=7.

Ответ:

\[2y^{2} + 7y + y^{2} - 24 = 0\]

\[3y^{2} + 7y - 24 = 0\]

\[D = 49 + 288 = 337\]

\[y_{1} = \frac{- 7 + \sqrt{337}}{6};\ \ \ \ \]

\[y_{2} = \frac{- 7 - \sqrt{337}}{6}\]

\[x_{1,2} = 2 \cdot \frac{- 7 \pm \sqrt{337}}{6} + 7 =\]

\[= \frac{- 7 \pm \sqrt{337} + 21}{3} =\]

\[= \frac{14 \pm \sqrt{337}}{3}.\]

\[Ответ:\left( \frac{14 \pm \sqrt{337}}{3};\ \frac{- 7 \pm \sqrt{337}}{6} \right).\]