Question

$solve \: the \: above \: equation \:$
​

Answer 1

Solution :-

2/x² - 5/x + 2 = 0

• Transposing 2 to RHS

2/x² - 5/x = -2

• By taking LCM, We get :-

2 - 5x / x² = -2

2x - 5x = -2x²

2x - 5x + 2x² = 0

• Arrange the given numbers in proper format

2x² - 5x + 2 = 0

2x² - 5x + 2 = 0

• By factorization method :-

2x² - 4x - x + 2 = 0

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

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

The value of x is 1/ 2 or 2 $.$

Answer 2

Given:

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

Solution:

$\frac{2}{ {x}^{2} } - \frac{5}{x} + 2 = 0 \\ \frac{2 - 5x + {2x}^{2} }{ {x}^{2} } = 0 \\ {2x}^{2} - 5x + 2 = 0 \\ on \: further \: factorisation \\ {2x}^{2} - x + 4x + 2 = 0 \\ x(2x - 1) - 2(2x - 1) = 0 \\ (x - 2)(2x - 1) = 0 \\ \\ either \\ x - 2 = 0 \\ x = 1 \: \: \: \: \: \: \: \: \: \: \: \: \: \: ans \\ \\ or \\ 2x - 1 = 0 \\ x = \frac{1}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: ans$