Question

please slove and give fast​

Answer 1

Step-by-step explanation:

Ww have,

$\sqrt{ \frac{x}{x - 3} } + \sqrt{ \frac{x - 3}{x} } = \frac{5}{2}$

$let \: \: y = \sqrt{ \frac{x}{x - 3} }$

$= > y + \frac{1}{y} = \frac{5}{2}$

$= > {y}^{2} + 1 = \frac{5y}{2}$

$= > 2 {y}^{2} - 5y + 2 = 0$

$= > 2 {y}^{2} - 4y - y + 2 = 0$

$= > 2y(y - 2) - 1(y - 2) = 0$

$= > (y - 2)(2y - 1) = 0$

$= > y = 2 \: \: or \: \: y = \frac{1}{2}$

$= > \sqrt{ \frac{x}{x - 3} } = 2 \: \: or \: \: \sqrt{ \frac{x}{x - 3} } = \frac{1}{2}$

$= > \frac{x}{x - 3} = 4 \: \: or \: \: \frac{x}{x - 3} = \frac{1}{4}$

$= > x = 4x - 12 \: \: or \: \: 4x = x - 3$

$= > 3x = 12 \: \: or \: \: 3x = - 3$

$= > x = 4 \: \: or \: \: x = - 1$