$f\left(x + \frac1x\right)= x^3+x^{-3},$ find $f(x)$ $$f\left(x + \frac1x\right)= x^3+x^{-3},$$ find $f(x)$.
What i do know at this state is that..
express x as a function of y :
$y= x + 1/x$
$x^2−xy+1=0$
Quad formula: 
$x= (y ± \sqrt {y^2-4}) / 2$
When i substitute this into the original equation, i can't solve it.

$x^3+x^{-3}=(x + \frac{1}{x})^3-3(x + \frac{1}{x})$
set $t=x + \frac{1}{x}, f(t)= t^3-3t$.
