Systems of Equations · Challenge problem

For every pair of numbers $x$ and $y$ with $x + y = m$ and $xy = n$, express each of the following in terms of $m$ and $n$ alone.

$(a)\ (x-y)^2$ $(b)\ \dfrac{x}{y} + \dfrac{y}{x}$ $(c)\ x^3 + y^3$