Systems of Equations · Challenge problem

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

$(a)\ (x-y)^2$ $(b)\ \dfrac{1}{x} + \dfrac{1}{y}$ $(c)\ \dfrac{x}{y} + \dfrac{y}{x}$