Question

If $x-\frac{1}{x}=2$, find $x^4+\frac{1}{x^4}$

Answer 1

Let $x-\frac{1}{x}=2$

Now squaring both sides we get,

$x^2-2+\frac{1}{x^2}=4$

or, $x^2+\frac{1}{x^2}=6$

Now again squaring we have,

$x^4+\frac{1}{x^4}+2=36$

or, $x^4+\frac{1}{x^4}=34$.