Math, asked by arnavgodofmischief, 9 months ago

if
x +  \frac{1}{x}  = 5,then
 \sqrt{x}  +  \frac{1}{ \sqrt{x} }
is equal to​

Answers

Answered by rkuntal7686
2

Step-by-step explanation:

x +  \frac{1}{x} = 5

add 2 to both sides

x +  \frac{1}{x} + 2 = 5 + 2

x+2.x.\frac{1}{x}+\frac{1}{x}=7

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

 \sqrt{x} +  \frac{1}{ \sqrt{x} } =  \sqrt{7}

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Answered by anindyaadhikari13
3

Given,

x +  \frac{1}{x}  = 5

Adding 2 to both the side, we get,

x +  \frac{1}{x}  + 2 = 7

Or,

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

Or,

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

Or,

 \sqrt{x}  +  \sqrt{ \frac{1}{x} }  = ± \sqrt{7}

Therefore, the correct answer is ±\sqrt{7}

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