Question

If x
$= 2 + \sqrt{3 \: } then \: find \: the \: value \: of \: {x}^{3} + \frac{1}{ {x}^{3} }$
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Answer 1

$\huge\color{cyan}\boxed{\colorbox{black}{ANSWER ❤}}$

We know that :

• $x = 2 + \sqrt{3}$

Now,

${x}^{3} + \frac{1}{ {x}^{3} }$

${(2 + \sqrt{3} )}^{3} + \frac{1}{ {(2 + \sqrt{3}) }^{3} }$

$26 + 15 \sqrt{3} + \frac{1}{26 + 15 \sqrt{3} }$

$26 + 15 \sqrt{3 } + \frac{1(26 - 15 \sqrt{3} )}{(26 + 15 \sqrt{3} )(26 - 15 \sqrt{3}) }$

$26 + 15 \sqrt{3} + \frac{26 - 15 \sqrt{3} }{676 - 675}$

$26 + 15 \sqrt{3} + 26 - 15 \sqrt{3}$

$26 + 26$

$52$

$26 + 15 \sqrt{3} + \frac{26 - 15 \sqrt{3} }{442}$

Answer by *BIG BRAIN*