Solution
We have : $$x^4+\frac{1}{x^4}=1442$$
Therefore we get $$\left(x^2\right)^{^2}+\left(\frac{1}{x^2}\right)^{^2}+2=1442+2\ =\ 1444$$
we get $$\left(x^2+\frac{1}{x^2}\right)^{^2}=\ 1444$$
Therefore $$x^2+\frac{1}{x^2}=38$$
Now $$x^2+\frac{1}{x^2}-2=36$$
we get $$\left(x-\frac{1}{x}\right)^{^2}=36$$
$$x-\frac{1}{x}=6$$
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