Question

x+1/x =5 then (x)^1/2 +(1/x)^1/2 =?

Answer 1

hey mate
here's the solution

Answer 2

✍✍HERE IS YOUR ANSWER..⬇⬇
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$\underline{SOLUTION}$ ➡

$\underline{Given \: :} \: \: \: x + \frac{1}{x} = 5 \\ \\ \\ \underline{To \: \: find \: :} \: \: (x ){}^{ \frac{1}{2} } +( \frac{1}{x} ) {}^{ \frac{1}{2} }$

$Now, \\ \\( \sqrt{x} + \frac{1}{ \sqrt{x} } ) {}^{2} \\ \\ = ( \sqrt{x} ) {}^{2} + 2 \times \sqrt{x} \times \frac{1}{ \sqrt{x} } + (\frac{1}{ \sqrt{x} } ) {}^{2} \\ \\ = x + 2 + \frac{1}{x} \\ \\ = x + \frac{1}{x} + 2 \\ \\ = 5 + 2 \\ \\ = 7 \\ \\ So ,\\ \\ ( \sqrt{x} + \frac{1}{ \sqrt{x} } ) {}^{2} = 7 \\ \\ = > \sqrt{x} + \frac{1}{ \sqrt{x} } = \sqrt{7} \\ \\ = > (x ){}^{ \frac{1}{2} } + ( \frac{1}{x} ) {}^{ \frac{1}{2} } = \sqrt{7} \: \: \: [As \: \: \sqrt{a }=( a ){}^{ \frac{1}{2} }]$

$\underline{ANSWER}$ ➡

$\boxed{(x ) {}^{ \frac{1}{2} } + (\frac{1}{x} ) {}^{ \frac{1}{2} } = \sqrt{7}}$

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