<s>[INST] $f\left(x + \frac1x\right)= x^3+x^{-3},$ 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.
 [/INST] Hint: $$\left(x + \frac1x\right)^3=x^3+3x^2\frac1x+3x\frac{1}{x^2}+\frac{1}{x^3}$$
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