Question

Solve for x:

Step-by-step

Answer 1

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Answer 2

$\sqrt{ \frac{1 - x}{x} } + \sqrt{ \frac{x}{1 - x} } = \frac{13}{6} \\ let \: \frac{1 - x}{x} = t \\ \sqrt{t } + \frac{1}{ \sqrt{t} } = \frac{13}{6} \\ = > 6t - 13 \sqrt{t} + 6 = 0 \\ let \: \sqrt{t} = a \\ = > 6a {}^{2} - 13a + 6 = 0 \\ = > a = \frac{3}{2} \: or \: \frac{2}{3} \\ so \: \sqrt{t} = \frac{3}{2} \: or \: \frac{2}{3} \\ \\ \\ therefore \: \frac{1 - x}{x} = \frac{9}{4} \: or \: \frac{4}{9} \\ sol ving \: this \\ x = \frac{4}{13} \: or \: \frac{9}{13}$

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