Solve this system equation:
2x^2 y^2 - 9y - 108 = 0
x + y + 3 = 0
You asked:
MathBot Answer:
The system of equations has \(4\) solutions.
\[x = - \frac{3}{2} - \frac{\sqrt{- \frac{27}{\sqrt[3]{- \frac{1971}{64} + \frac{27 \sqrt{19153}}{64}}} + 3 + 2 \sqrt[3]{- \frac{1971}{64} + \frac{27 \sqrt{19153}}{64}}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{- \frac{1971}{64} + \frac{27 \sqrt{19153}}{64}} + 6 + \frac{27}{\sqrt[3]{- \frac{1971}{64} + \frac{27 \sqrt{19153}}{64}}} + \frac{9}{\sqrt{- \frac{27}{\sqrt[3]{- \frac{1971}{64} + \frac{27 \sqrt{19153}}{64}}} + 3 + 2 \sqrt[3]{- \frac{1971}{64} + \frac{27 \sqrt{19153}}{64}}}}}}{2}, y = - \frac{\sqrt{- 2 \sqrt[3]{- \frac{1971}{64} + \frac{27 \sqrt{19153}}{64}} + 6 + \frac{27}{\sqrt[3]{- \frac{1971}{64} + \frac{27 \sqrt{19153}}{64}}} + \frac{9}{\sqrt{- \frac{27}{\sqrt[3]{- \frac{1971}{64} + \frac{27 \sqrt{19153}}{64}}} + 3 + 2 \sqrt[3]{- \frac{1971}{64} + \frac{27 \sqrt{19153}}{64}}}}}}{2} - \frac{3}{2} + \frac{\sqrt{- \frac{27}{\sqrt[3]{- \frac{1971}{64} + \frac{27 \sqrt{19153}}{64}}} + 3 + 2 \sqrt[3]{- \frac{1971}{64} + \frac{27 \sqrt{19153}}{64}}}}{2}\]\[x = - \frac{3}{2} + \frac{\sqrt{- \frac{27}{\sqrt[3]{- \frac{1971}{64} + \frac{27 \sqrt{19153}}{64}}} + 3 + 2 \sqrt[3]{- \frac{1971}{64} + \frac{27 \sqrt{19153}}{64}}}}{2} - \frac{\sqrt{- \frac{9}{\sqrt{- \frac{27}{\sqrt[3]{- \frac{1971}{64} + \frac{27 \sqrt{19153}}{64}}} + 3 + 2 \sqrt[3]{- \frac{1971}{64} + \frac{27 \sqrt{19153}}{64}}}} - 2 \sqrt[3]{- \frac{1971}{64} + \frac{27 \sqrt{19153}}{64}} + 6 + \frac{27}{\sqrt[3]{- \frac{1971}{64} + \frac{27 \sqrt{19153}}{64}}}}}{2}, y = - \frac{3}{2} - \frac{\sqrt{- \frac{27}{\sqrt[3]{- \frac{1971}{64} + \frac{27 \sqrt{19153}}{64}}} + 3 + 2 \sqrt[3]{- \frac{1971}{64} + \frac{27 \sqrt{19153}}{64}}}}{2} + \frac{\sqrt{- \frac{9}{\sqrt{- \frac{27}{\sqrt[3]{- \frac{1971}{64} + \frac{27 \sqrt{19153}}{64}}} + 3 + 2 \sqrt[3]{- \frac{1971}{64} + \frac{27 \sqrt{19153}}{64}}}} - 2 \sqrt[3]{- \frac{1971}{64} + \frac{27 \sqrt{19153}}{64}} + 6 + \frac{27}{\sqrt[3]{- \frac{1971}{64} + \frac{27 \sqrt{19153}}{64}}}}}{2}\]\[x = - \frac{3}{2} + \frac{\sqrt{- \frac{27}{\sqrt[3]{- \frac{1971}{64} + \frac{27 \sqrt{19153}}{64}}} + 3 + 2 \sqrt[3]{- \frac{1971}{64} + \frac{27 \sqrt{19153}}{64}}}}{2} + \frac{\sqrt{- \frac{9}{\sqrt{- \frac{27}{\sqrt[3]{- \frac{1971}{64} + \frac{27 \sqrt{19153}}{64}}} + 3 + 2 \sqrt[3]{- \frac{1971}{64} + \frac{27 \sqrt{19153}}{64}}}} - 2 \sqrt[3]{- \frac{1971}{64} + \frac{27 \sqrt{19153}}{64}} + 6 + \frac{27}{\sqrt[3]{- \frac{1971}{64} + \frac{27 \sqrt{19153}}{64}}}}}{2}, y = - \frac{3}{2} - \frac{\sqrt{- \frac{27}{\sqrt[3]{- \frac{1971}{64} + \frac{27 \sqrt{19153}}{64}}} + 3 + 2 \sqrt[3]{- \frac{1971}{64} + \frac{27 \sqrt{19153}}{64}}}}{2} - \frac{\sqrt{- \frac{9}{\sqrt{- \frac{27}{\sqrt[3]{- \frac{1971}{64} + \frac{27 \sqrt{19153}}{64}}} + 3 + 2 \sqrt[3]{- \frac{1971}{64} + \frac{27 \sqrt{19153}}{64}}}} - 2 \sqrt[3]{- \frac{1971}{64} + \frac{27 \sqrt{19153}}{64}} + 6 + \frac{27}{\sqrt[3]{- \frac{1971}{64} + \frac{27 \sqrt{19153}}{64}}}}}{2}\]\[x = - \frac{\sqrt{- 2 \sqrt[3]{- \frac{1971}{64} + \frac{27 \sqrt{19153}}{64}} + 6 + \frac{27}{\sqrt[3]{- \frac{1971}{64} + \frac{27 \sqrt{19153}}{64}}} + \frac{9}{\sqrt{- \frac{27}{\sqrt[3]{- \frac{1971}{64} + \frac{27 \sqrt{19153}}{64}}} + 3 + 2 \sqrt[3]{- \frac{1971}{64} + \frac{27 \sqrt{19153}}{64}}}}}}{2} - \frac{3}{2} - \frac{\sqrt{- \frac{27}{\sqrt[3]{- \frac{1971}{64} + \frac{27 \sqrt{19153}}{64}}} + 3 + 2 \sqrt[3]{- \frac{1971}{64} + \frac{27 \sqrt{19153}}{64}}}}{2}, y = - \frac{3}{2} + \frac{\sqrt{- \frac{27}{\sqrt[3]{- \frac{1971}{64} + \frac{27 \sqrt{19153}}{64}}} + 3 + 2 \sqrt[3]{- \frac{1971}{64} + \frac{27 \sqrt{19153}}{64}}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{- \frac{1971}{64} + \frac{27 \sqrt{19153}}{64}} + 6 + \frac{27}{\sqrt[3]{- \frac{1971}{64} + \frac{27 \sqrt{19153}}{64}}} + \frac{9}{\sqrt{- \frac{27}{\sqrt[3]{- \frac{1971}{64} + \frac{27 \sqrt{19153}}{64}}} + 3 + 2 \sqrt[3]{- \frac{1971}{64} + \frac{27 \sqrt{19153}}{64}}}}}}{2}\]