Solve this
Question:

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

Solution:

Given:

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

$\Rightarrow 2-5 x+2 x^{2}=0 \quad$ [Multiplying both side by $\left.x^{2}\right]$

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

$\Rightarrow 2 x^{2}-(4 x+x)+2=0$

$\Rightarrow 2 x^{2}-4 x-x+2=0$

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

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

$\Rightarrow 2 x-1=0$ or $x-2=0$

$\Rightarrow x=\frac{1}{2}$ or $x=2$

Hence, the roots of the equation are $\frac{1}{2}$ and 2 .

 

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