Math, asked by Iqrakafeel9190, 10 months ago

If x=√2 find the value of (x+1/x) ^4

Answers

Answered by Mihir1001

$\huge{\underline{\mathfrak{\textcolor{blue}{Answer :}}}}$

$\huge\boxed{\fcolorbox{red}{#ffdfff}{81/4}}$

$\LARGE{\underline{\mathrm{\textcolor{red}{Step-by-step \: \: explanation :}}}}$

$\Large{\underline{\mathtt{\textcolor{violet}{Given :}}}}$

$x = \sqrt{2}$

$\Large{\underline{\mathtt{\textcolor{green}{To \: find :}}}}$

${(x + \frac{1}{x} )}^{4}$

$\Large{\underline{\mathtt{\textcolor{blue}{Solution :}}}}$

let's start with second equation.

We have,

${(x + \frac{1}{x} )}^{4}$

$= {( \sqrt{2} + \frac{1}{ \sqrt{2} } )}^{4}$

$= {( \frac{( \sqrt{2} )( \sqrt{2} ) + 1}{ \sqrt{2} } )}^{4}$

$= {( \frac{2 + 1}{ \sqrt{2} } )}^{4}$

$= {( \frac{3}{ \sqrt{2} } )}^{4}$

$= \frac{ {(3)}^{4} }{ {( \sqrt{2} )}^{4} }$

$= \frac{3 \times 3 \times 3 \times 3}{ \sqrt{2} \times \sqrt{2} \times \sqrt{2} \times \sqrt{2} }$

$= \frac{9 \times 9}{2 \times 2}$

$= \frac{81}{4}$

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Answered by MihirRaj11

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