x^2 = 6*sqrt(x^2 - 4)
You asked:
Solve the equation \({x}^{2} = 6 \sqrt{{x}^{2} - 4}\) for the variable \(x\).
MathBot Answer:
The 4 solutions to the equation are: \[\begin{aligned}x &= - 2 \sqrt{\frac{9}{2} - \frac{3 \sqrt{5}}{2}} \approx -2.1409325\\x &= 2 \sqrt{\frac{9}{2} - \frac{3 \sqrt{5}}{2}} \approx 2.1409325\\x &= - 2 \sqrt{\frac{9}{2} + \frac{3 \sqrt{5}}{2}} \approx -5.6050342\\x &= 2 \sqrt{\frac{9}{2} + \frac{3 \sqrt{5}}{2}} \approx 5.6050342\end{aligned}\]