If x2 + 1/x2 = 66, find the value of x − 1/x

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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