Question

Please give me its answer within 2 minutes

Answer 1

Answes 18
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Answer 2

$\textbf{ \underline{ Hello Mate! }}$

$x = 2 - \sqrt{5} \\ \frac{1}{x} = \frac{1}{2 - \sqrt{5} } \\ rationalize \\ \frac{1}{2 - \sqrt{5} } \times \frac{2 + \sqrt{5} }{2 + \sqrt{5} } \\ = \frac{2 + \sqrt{5} }{ {2}^{2} - { \sqrt{5} }^{2} } = \frac{2 + \sqrt{5} }{4 - 5} \\ = \frac{2 + \sqrt{5} }{ - 1} \: or \: - 2 - \sqrt{5} \\ {x }^{2} = {(2 - \sqrt{5} )}^{2} \\ = 4 + 5 - 4 \sqrt{5} = 9 - 4 \sqrt{5} \\ {( \frac{1}{x}) }^{2} = {( - 2 - \sqrt{5}) }^{2} \\ = 4 + 5 - 2 \times ( - 2) \times ( \sqrt{5} ) \\ = 9 + 4 \sqrt{5} \\ {x}^{2} + {( \frac{1}{x} )}^{2} = \\ = 9 - 4 \sqrt{5} + 9 + 4 \sqrt{5} \\ = 18$
$\boxed{ Hence\:answer\:is\:18 }$

Have great future ahead!