Question

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

Answer 1

$x+\frac{1}{x}=3x\ne 0$

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

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

$\Rightarrow x^2+\frac{9}{4}-2\left(\frac{3}{2}\right)x=\frac{5}{4}$

$\Rightarrow {(x-\frac{3}{2})}^2={\left(\frac{\sqrt{5}}{2}\right)}^2$

$\Rightarrow x=\frac{3}{2}\pm \frac{\sqrt{5}}{2}$