Systems of Equations · Challenge problem

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

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