xy = 200

x^2 - y^2 = 96

asked by guest
on Oct 22, 2024 at 4:19 pm



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 \(i^2 = -1\).

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