Question

Root2+1FIND(x+1÷x)^2

Answer 1

Hope u like my process
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$= > \: \: x = \sqrt{2} + 1 \\ \\ = > \: \: \frac{1}{ {x}} = \frac{ 1}{ \sqrt{2} + 1 } = \frac{( \sqrt{2} - 1) }{( \sqrt{2} - 1)( \sqrt{2} + 1) } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{ \sqrt{2} - 1 }{ {( \sqrt{2}) }^{2} - {1}^{2} } = \frac{ \sqrt{2} - 1 }{2 - 1} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \sqrt{2 } - 1$
Now..
$= > \: {(x + \frac{1}{x} )}^{2} \\ \\ = {( (\sqrt{2} + 1) + ( \sqrt{2} - 1) )}^{2} \\ \\ = {( \sqrt{2} + 1 + \sqrt{2} - 1) }^{2} \\ \\ = {(2 \sqrt{2} )}^{2} = 8....answer....$
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Hope this is ur required answer
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