Question

X2+1/X2=8 find X2-1/X2
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Answer 1

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$\underline{\large\mathcal\red{solution}}$

$x {}^{2} + \frac{1}{x {}^{2} } = 8 \\ \: now \: \: \: \\ (x {}^{2} - \frac{1}{x {}^{2} } ) {}^{2} = (x {}^{2} + \frac{1}{x {}^{2} } ){}^{2}- 4( \frac{1}{x {}^{2} } )(x {}^{2} ) \\ = > (x {}^{2} - \frac{1}{x {}^{2} } ) {}^{2} = 8 {}^{2} - 4 \\ = > (x {}^{2} - \frac{1}{x {}^{2} }) = \sqrt{60} = 2 \sqrt{15}$

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Answer 2

$\underline{\mathcal\blue{Answer:-}}$

$\begin{lgathered}x {}^{2} + \frac{1}{x {}^{2} } = 8 \\ \: now \: \: \: \\ (x {}^{2} - \frac{1}{x {}^{2} } ) {}^{2} = (x {}^{2} + \frac{1}{x {}^{2} } ){}^{2}- 4( \frac{1}{x {}^{2} } )(x {}^{2} ) \\ (x {}^{2} - \frac{1}{x {}^{2} } ) {}^{2} = 8 {}^{2} - 4 \\ (x {}^{2} - \frac{1}{x {}^{2} }) = \sqrt{60} = 2 \sqrt{15}\end{lgathered} </p><p>$