Systems of Equations · Challenge problem

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

$(a)\ \dfrac{x}{y} + \dfrac{y}{x}$ $(b)\ x^4 + y^4$ $(c)\ x^2 + y^2$