Question

If x= √5+2 then find X square -1/xsquare

Answer 1

$x = \sqrt{5} + 2 \\ \frac{1}{x} = \frac{1}{ \sqrt{5 } + 2 } = \frac{1}{ \sqrt{5} + 2} \times \frac{ \sqrt{5} - 2}{ \sqrt{5} - 2 } \\ = \frac{ \sqrt{5} - 2}{ (\sqrt{5}) {}^{2} - 2 {}^{2} } = \frac{ \sqrt{5} - 2 }{5 - 4} = \sqrt{5} - 2$
$x {}^{2} - \frac{1}{x {}^{2} } = (x + \frac{1}{x} )(x - \frac{1}{x} ) \\ = (\sqrt{5} + 2 + \sqrt{5} - 2) \\ \: \: \: \: ( \sqrt{5} + 2 - \sqrt{5} + 2) \\ = 2 \sqrt{5} \times 4 \\ = 8 \sqrt{5}$

Answer 2

Hey !!!! Your answer =>

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