Question

Find the roots of the equation:

$x-\frac{1}{x}=3,x\ne 0$

Answer 1

$\begin{array}{c}x-\frac{1}{x}=3\\ \frac{x^2-1}{x}=3\\ x^2-1=3x\\ x^2-3x-1=0\\ x=\frac{3\pm \sqrt{3^2-\left(9\right)\left(-1\right)}}{2}\\ x=\frac{3\pm \sqrt{13}}{2}\end{array}$