Question

2/x²-5/x+2=0 ( x not equals to 0 )​

Answer 1

$\large \green{ \underline { \sf \: Given :-}}$

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

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

$\sf : \implies 2 {x}^{2} - 5x + 2 = 0$

$\sf : \implies 2 {x}^{2} - 4x - x + 2 = 0$

$\sf : \implies 2x(x - 2) - 1(x - 2) = 0$

$\sf : \implies (2x - 1)(x - 2) = 0$

$\sf : \implies 2x - 1 = 0$

$\sf : \implies \green{ \boxed{ \sf \: x = \frac{1}{2} }}$

$\sf : \implies x - 2 = 0$

$\sf : \implies \green{ \boxed{ \sf x = 2}}$