Solve equation by factorization : 2 x^2 -5 x +2=0, x 0 - Vidyadip

Question

Solve equation by factorization : $\frac{2}{x^2}-\frac{5}{x}+2=0, x \neq 0$

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Answer

$ \frac{2}{x^2}-\frac{5}{x}+2=0, x \neq 0$
$ \Rightarrow 2-5 x+2 x^2=0$
$ \Rightarrow 2 x^2-5 x+2=0 \ldots$
$\because 2 \times 2=4$
$4=-4 \times(-1)-5=-4-1$
$ \Rightarrow 2 x^2-4 x-x+2=0$
$ \Rightarrow 2 x(x-2)-1(x-2)=0$
$ \Rightarrow(x-2)(2 x-1)=0$
$ \text { Either } x-2=0$
$ \text { then } x=2$
$ \text { or }$
$ 2 x =1=0$
$ \text { then } 2 x=1$
$ \Rightarrow x=\frac{1}{2}$
$ \therefore x=2, \frac{1}{2} .$

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