Question

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

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$\frac{ {x + 1}^{2} }{ {x}^{2} }$

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$x = \sqrt{5} + 2$

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$\frac{ {x}^{2} + 1 }{ {x}^{2} }$

$= \: \frac{ (\sqrt{5} + 2 ) { }^{2} + 1}{( \sqrt{5} + 2) {}^{2} }$

$= \frac{( \sqrt{5} ) {}^{2} + (2) {}^{2} + 2( \sqrt{5})(2) \: \: \: + \: \: 1 \: \: \: }{ ( \sqrt{5} ) {}^{2} + (2) {}^{2} + 2( \sqrt{5} )(2)}$

$= \frac{5 + 4 + 4 \sqrt{5} \: \: + 1}{5 + 4 + 4 \sqrt{5} }$

$= \frac{10 + 4 \sqrt{5} }{9 + 4 \sqrt{5} }$

Answer 2

Answer:

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