x+y=-5

x^2+y^3=5

asked by guest
on Nov 25, 2024 at 4:29 am



You asked:

Solve the system of equations:\[\begin{aligned}x + y &= -5\\{x}^{2} + {y}^{3} &= 5\end{aligned}\]

MathBot Answer:

The system of equations has \(3\) solutions.

\[x = \frac{- 14 \left(226 + 3 \sqrt{8385}\right)^{\frac{2}{3}} - 29 \sqrt[3]{226 + 3 \sqrt{8385}} + 226 + 3 \sqrt{8385}}{3 \left(226 + 3 \sqrt{8385}\right)^{\frac{2}{3}}}, y = - \frac{\sqrt[3]{226 + 3 \sqrt{8385}}}{3} - \frac{1}{3} + \frac{29}{3 \sqrt[3]{226 + 3 \sqrt{8385}}}\]\[x = \frac{- 14 \sqrt{3} \left(226 + 3 \sqrt{8385}\right)^{\frac{2}{3}} + 29 \sqrt{3} \sqrt[3]{226 + 3 \sqrt{8385}} - 14 i \left(226 + 3 \sqrt{8385}\right)^{\frac{2}{3}} - 6 \sqrt{8385} i - 452 i - 29 i \sqrt[3]{226 + 3 \sqrt{8385}}}{3 \left(226 + 3 \sqrt{8385}\right)^{\frac{2}{3}} \left(\sqrt{3} + i\right)}, y = - \frac{1}{3} + \frac{29}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{226 + 3 \sqrt{8385}}} - \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{226 + 3 \sqrt{8385}}}{3}\]\[x = \frac{- 14 \sqrt{3} \left(226 + 3 \sqrt{8385}\right)^{\frac{2}{3}} + 29 \sqrt{3} \sqrt[3]{226 + 3 \sqrt{8385}} + 29 i \sqrt[3]{226 + 3 \sqrt{8385}} + 452 i + 6 \sqrt{8385} i + 14 i \left(226 + 3 \sqrt{8385}\right)^{\frac{2}{3}}}{3 \left(226 + 3 \sqrt{8385}\right)^{\frac{2}{3}} \left(\sqrt{3} - i\right)}, y = - \frac{1}{3} - \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{226 + 3 \sqrt{8385}}}{3} + \frac{29}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{226 + 3 \sqrt{8385}}}\]

\(i\) is the imaginary unit, defined as \(i^2 = -1\).

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