Question

please answer, it is very urgent​

Answer 1

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Answer 2

$hi \: frien d....$

$here \: ...$

$x = 2 + \sqrt{3}$

${x}^{2} = ( {2 + \sqrt{3} )}^{2}$

${x}^{2} = {2}^{2} + 2(2)( \sqrt{3)} + { \sqrt{3} }^{2}$

${x}^{2} = 4 + 4 \sqrt{3} + 3$

${x}^{2} = 7 + 4 \sqrt{3}$

Now ,

${x}^{2} + \frac{1}{ {x}^{2} } \\ = 7 + 4 \sqrt{3} + \frac{1}{7 + 4 \sqrt{3} }$

$= \frac{( {7 + 4 \sqrt{3} )}^{2} + 1 }{7 + 4 \sqrt{3} }$

$= \frac{49 + 2(7)(4 \sqrt{3) } + {4 \sqrt{3} }^{2} + 1}{7 + 4 \sqrt{3} }$

$= \frac{49 + 56 \sqrt{3} + 48 + 1}{7 + 4 \sqrt{3} }$

$= \frac{98 + 56 \sqrt{3} }{7 + 4 \sqrt{3} }$

$= 14 \: (approx)$

$hope \: it \: helps \: you \:$

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