Question

√x/x-3+√x-3/x=5/2, when x is not equal to 0 and 3

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Answer 1

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$\huge \purple\bigstar \underline {\pink {\boxed {question}}} \purple\bigstar$

$= > \sqrt{ \frac{x}{x - 3} } + \sqrt{ \frac{x - 3}{x} } = \frac{5}{2} is \: not \: equal \: to \: 0 \: and \: 3$

$\blue{LET,}$

$\orange{\sqrt{ \frac{x}{x - 3} } = t}$

$t + \frac{1}{t} = \frac{5}{2}$

$\pink{ {t}^{2} + 1} = \purple{ \frac{5}{2} }$

$\mathbf \green{ 2 {t}^{2} - 5t + 2 = 0}$

$\mathfrak \red { 2 {t}^{2} (t - 2) - 1(t - 2)} = 0$

$(2t - 1)(t - 2) = 0$

$t = \frac{1}{2} \: \: or \: \: \: 2$

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

$\mathtt{\pink{\frac{x}{x - 3} = \frac{1}{4}} \: \: \: \: or \: \: \: \: \blue{ \frac{x}{x - 3} = 4}}$

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

There, are two values of x as below:-

x= -1 x=4