Question

√(x/x+1) +√(x+1/x) =5/2

plz solve this question ​

Answer 1

$\sqrt{ \frac{x}{x + 1} } + \sqrt{ \frac{x + 1}{x} } = \frac{5}{2}$

$\frac{ \sqrt{ {x }^{2} } + \sqrt{ {x}^{2} } + 1 + 2x}{(x + 1)x} = \frac{5}{2}$

$\frac{ \sqrt{ {x}^{2} } + \sqrt{} {x}^{2} + 2x + 1}{ {x}^{2} + x} = \frac{5}{2}$

$\frac{2x + 1}{ {x}^{2} + x } = \frac{5}{2}$

$2(2x + 1) = 5( {x}^{2} + x)$

$4x + 2 = 5 {x}^{2} + 5x$

$4x - 5x + 2 = 5 {x}^{2}$

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

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