Solve equation using factorisation method: x+1 x =2.5 - Vidyadip

Question

Solve equation using factorisation method:
$x+\frac{1}{x}=2.5$

✓

Answer

$x+\frac{1}{x}=2.5$
$\Rightarrow \frac{x^2+1}{x}=\frac{5}{2}$
$\Rightarrow 2 x^2+2=5 x$
$\Rightarrow 2 x^2-5 x+2=0$
$\Rightarrow 2 x(x-2)-1(x-2)=0$
$\Rightarrow(x-2)(2 x-1)=0$
Since $x - 2 = 0$ or $2x - 1 = 0$
$\therefore x - 2 = 0$
$\Rightarrow x = 2$
$\therefore 2x - 1 = 0$
$\Rightarrow 2x = 1$
$\Rightarrow x=\frac{1}{2}$
then $x =2$ or $x =\frac{1}{2}$

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