Let $K\supseteq F$ be a field extension and $x,y\in F$. Can someone please explain to why the equivalence $ x,y\text{ algebraic over }F\ \Leftrightarrow\ x+y\text{ and }xy\text{ are algebraic over }F $ should hold ?
(the $\Rightarrow$ direction is fairly easy, and I did it, but I'm stuck at the other direction.)