Systems of Equations · Challenge problem

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

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