How to find $1/x^3 + 1/y^3$? If I am given, $x + y = a$  and $xy = b$, how would I find the value of $\dfrac1{x^3} + \dfrac1{y^3}$?

\begin{align}
\dfrac1{x^3} + \dfrac1{y^3} & = \dfrac{x^3+y^3}{(xy)^3} = \dfrac{\left(x+y \right)\left(x^2+y^2-xy \right)}{(xy)^3}\\
& = \dfrac{\left(x+y \right)\left(\left(x+y \right)^2-3xy \right)}{(xy)^3}  = \dfrac{a\left(a^2-3b \right)}{b^3}
\end{align}
