Given that $ x + \frac 1 x = r $ what is the value of: $ x^3 + \frac 1 {x^2}$ in terms of $r$? Given that $$ x + \cfrac 1 x = r $$
what is the value of: $$ x^3 + \cfrac 1 {x^2}$$ in terms of $r$?
NOTE: it is $\cfrac 1 {x^2}$ and not $ \cfrac 1 {x^3} $
Where I reached so far:
$$ \Big(x^3 + \cfrac 1 {x^2}\Big) + \cfrac 1 x \cdot\Big(x^3 + \cfrac 1 {x^2}\Big) = r^3 - r^2 -3r - 2 $$
Any hints??

If $g$ is a function such that $g(x)=f(x+\frac{1}{x})$ then $g(1/x)=g(x)$. 
Your $g(x)=x^3+x^{-2}$ therefore cannot be written as $f(x+1/x)$.
