Question

√x/x-3+√x-3/x=5/2 what are the roots of the equation
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Answer 1

Answer:

➡️

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

Let

$\sqrt{ \frac{x}{x - 3} } = k$

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

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

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

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

let k=1/2

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

$4x = x - 3$

$x = - 1$

Let k=2

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

$x = 4x - 12$

$x = 4$

There fore x=-1 or 4.✅

Answer 2

Answer:

X = -1 OR X = 4

Step-by-step explanation:

Please see the attached image.

Hope it helps you.

Thanks !