xy = 200
x^2 - y^2 = 96
You asked:
Solve the system of equations:\[\begin{aligned}x y &= 200\\{x}^{2} - {y}^{2} &= 96\end{aligned}\]
MathBot Answer:
The system of equations has \(4\) solutions.
\[x = - \frac{\sqrt{-12 + 2 \sqrt{661}} \cdot \left(48 + 8 \sqrt{661}\right)}{100}, y = - 2 \sqrt{-12 + 2 \sqrt{661}}\]\[x = \frac{\sqrt{-12 + 2 \sqrt{661}} \cdot \left(48 + 8 \sqrt{661}\right)}{100}, y = 2 \sqrt{-12 + 2 \sqrt{661}}\]\[x = - \frac{i \sqrt{12 + 2 \sqrt{661}} \cdot \left(48 - 8 \sqrt{661}\right)}{100}, y = - 2 i \sqrt{12 + 2 \sqrt{661}}\]\[x = \frac{i \sqrt{12 + 2 \sqrt{661}} \cdot \left(48 - 8 \sqrt{661}\right)}{100}, y = 2 i \sqrt{12 + 2 \sqrt{661}}\]
\(i\) is the imaginary unit, defined as \(i^2 = -1\).