Question

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

Answer 1

✍✍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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Answer 2

Given Equation is x + 1/x = 5.

It can be written as,

⇒ x + 1/x = 7 - 2

⇒ x + 1/x + 2 = 7

⇒ (√x)^2 + (1/√x)^2 + 2(√x)(1/√x) = 7

⇒ (√x + 1/√x)^2 = 7

⇒ √x + 1/√x = ₊7,₋7

(or)

⇒ (x)^1/2 + (1/x)^1/2) = ₊7,₋7.

Hope it helps!