Question

Find the roots of the following equation using Quadratic formula:
$x-\frac{1}{x}=3,x\ne 0$

Answer 1

Solution:
$$\begin{array}{cc}& x-\frac{1}{x}=3\\ & \Rightarrow x^2-3x-1=0\end{array}$$
On comparing this equation with $a{x}^2+bx+c=0$,
we obtain $a=1,b=-3,c=1$
By using quadratic formula, we obtain
$$\begin{array}{cc}& \Rightarrow x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\ & \Rightarrow x=\frac{3\pm \sqrt{9+4}}{2}\\ & \Rightarrow x=\frac{3\pm \sqrt{13}}{2}\end{array}$$
Therefore, $x=\frac{3+\sqrt{13}}{2}$ or $\frac{3-\sqrt{13}}{2}$