If a +1 a =6;find a -1 a - Vidyadip

Question

If $a +\frac{1}{ a }=6$;find $a -\frac{1}{ a }$

✓

Answer

$\left(a+\frac{1}{a}\right)^2 $
$ =\left(a^2\right)+2(a)\left(\frac{1}{a}\right)+\left(\frac{1}{a}\right)^2 $
$ =a^2+\frac{1}{a^2}+2 $
$=36=a^2+\frac{1}{a^2}+2$
$=a^2+\frac{1}{a^2} $
$=34 $
$ \left(a-\frac{1}{a}\right)^2 $
$ =(a)^2-2(a)\left(\frac{1}{a}\right)+\left(\frac{1}{a}\right)^2 $
$ =a^2+\frac{1}{a^2}-2 $
$ =34-2$
$=32$
$ \Rightarrow a-\frac{1}{a} $
$ = \pm \sqrt{32} $
$ = \pm 4 \sqrt{2} .$

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