Question

Find the roots of the equation $x-\frac{1}{3x}=\frac{1}{6},(x\ne 0)$

Answer 1

Given,

$x-\frac{1}{3x}=\frac{1}{6}$

$⟹\frac{3x^2-1}{3x}=\frac{1}{6}$

$⟹18x^2-6=3x$

$⟹18x^2-3x-6=0$

$⟹6x^2-x-2=0$

$⟹6x^2-4x+3x-2=0$

$⟹2x(3x-2)+1(3x-2)=0$

$⟹(3x-2)(2x+1)=0$

$⟹x=\frac{2}{3},\frac{-1}{2}$