√7-√3/x=x/√7+√3
You asked:
Solve the equation \(\sqrt{7} - \frac{\sqrt{3}}{x} = \frac{x}{\sqrt{7}} + \sqrt{3}\) for the variable \(x\).
MathBot Answer:
The 2 solutions to the equation are: \[\begin{aligned}x &= - \frac{\sqrt{21}}{2} + \frac{7}{2} - \frac{\sqrt{2} i \sqrt{-35 + 9 \sqrt{21}}}{2} \approx 1.2087122 -1.7668024 i\\x &= - \frac{\sqrt{21}}{2} + \frac{7}{2} + \frac{\sqrt{2} i \sqrt{-35 + 9 \sqrt{21}}}{2} \approx 1.2087122 + 1.7668024 i\end{aligned}\]
\(i\) is the imaginary unit, defined as \(i^2 = -1\).