ÖMO 1990 Problem 3

In a convex quadrilateral $ABCD$ , let $E$ be the intersection point of the diagonals, and let $F_1,F_2,$ and $F$ be the areas of $ABE,CDE,$ and $ABCD,$ respectively. Prove that:

$\sqrt {F_1}+\sqrt {F_2} \le \sqrt {F}.$