Let $\displaystyle F\subset{E}$. both $\displaystyle E$ and $\displaystyle F$ are fields, $\displaystyle \alpha$,$\displaystyle \beta\in{E}$. If $\displaystyle \alpha+\beta$ and$\displaystyle \alpha\beta$ are algebraic over $\displaystyle F$, show that $\displaystyle \alpha$ and $\displaystyle \beta$ are algebraic