Question:
If $x^{2}+1 / x^{2}=66$, find the value of $x-1 / x$
Solution:
We have,
$(x-1 / x)^{2}=x^{2}+(1 / x)^{2}-2 * x * 1 / x$
$\Rightarrow(x-1 / x)^{2}=x^{2}+1 / x^{2}-2$
$\Rightarrow(x-1 / x)^{2}=66-2\left[\therefore x^{2}+1 / x^{2}=66\right]$
$\Rightarrow(x-1 / x)^{2}=64$
$\Rightarrow(x-1 / x)^{2}=(\pm 8)^{2}$
$\Rightarrow x-1 / x=\pm 8$
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