Question

if x=√5+2,then find the value of x²+1/x²​.
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Answer 1

$\mathfrak{\huge{Answer:-}}\\ x = \sqrt{5} + 2 \\ {x}^{2} + \frac{1}{ {x}^{2} } \\ = {( \sqrt{5} + 2) }^{2} + \frac{1}{ {( \sqrt{5} + 2)}^{2} } \\ = 5 + 4 + 4 \sqrt{5} + \frac{1}{5 + 4 + 4 \sqrt{5} } \\ = 9 + 4 \sqrt{5} + \frac{1}{9 + 4 \sqrt{5} } \\ = \frac{ {(9 + 4 \sqrt{5} )}^{2} + 1}{9 + 4 \sqrt{5} } \\ = \frac{81 + 80 + 72 \sqrt{5} + 1 }{9 + 4 \sqrt{5} } \\ = \frac{162 + 72 \sqrt{5} }{9 + 4 \sqrt{5} } \\ = \frac{18(9 + 4 \sqrt{5}) }{(9 + 4 \sqrt{5} )} \\ = 18 \\ \boxed{\boxed{\large{\bold{ {x}^{2} + \frac{1}{ {x}^{2} } = 18 }}}}$

Answer 2

Answer:

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Step-by-step explanation:

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