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.

$(a)\ x^3 + y^3$ $(b)\ \dfrac{1}{x} + \dfrac{1}{y}$ $(c)\ x^4 + y^4$