Question

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

Answer 1

Given,

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

$x^2-1=3x$

$x^2-3x-1=0$

$a=1,b=-3,c=-1$

$x=\frac{-(-3)\pm \sqrt{{(-3)}^2-4\cdot 1(-1)}}{2\cdot 1}$

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