Question

Solve $\frac{2}{x^2}-\frac{5}{x}+2=0$ by factorisation method. Find the roots of (PS)
$\frac{1}{x}-\frac{1}{x-2}=3x\ne 0,2$.

Answer 1

Given,

$\frac{2}{x^2}-\frac{5}{x}+2=0$

$2-5x+2x^2=0$

$2x^2-5x+2=0$

$(x-2)(2x-1)=0$

$x=2,\frac{1}{2}$

Given,

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

$x-2-x=3\left(x\right)(x-2)$

$-2=3x^2-6x$

$3x^2-6x+2=0$

$x=\frac{-(-6)\pm \sqrt{{(-6)}^2-4\cdot 3\cdot 2}}{2\cdot 3}$

$=\frac{6\pm \sqrt{12}}{6}$

$=\frac{2(3\pm \sqrt{3})}{6}$

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