Question

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

Answer 1

Given $x-\frac{1}{x}=-3$

$\Rightarrow \frac{x^2-1}{x}=-3$

$\Rightarrow x^2-1=-3x$

$\Rightarrow x^2+3x-1=0$

Using Shri Dharacharya method

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2z}$

$=\frac{-3\pm \sqrt{9-4\left(1\right)(-1)}}{2\left(1\right)}$

$=\frac{-3\pm \sqrt{13}}{2}$

$\therefore x=\frac{-3+\sqrt{13}}{2},\frac{-3-\sqrt{13}}{2}$

These are the required roots of the equation.