If a -1 a =10 ; find a ^2-1 a ^2 - Vidyadip

Question

If $a -\frac{1}{ a }=10 ;$ find $a ^2-\frac{1}{ a ^2}$

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Answer

$a ^2-\frac{1}{ a ^2} $
$=\left( a +\frac{1}{ a }\right)\left( a -\frac{1}{ a }\right) $
$ =( \pm 2 \sqrt{26})(10) $
$= \pm 20 \sqrt{26} .$

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