OME 2006 Problem 6

The diagonals $AC$ and $BD$ of a convex quadrilateral $ABCD$ intersect at $E$ . Denotes by $S_1,S_2$ and $S$ the areas of the triangles $ABE$ , $CDE$ and the quadrilateral $ABCD$ respectively. Prove that $\sqrt{S_1}+\sqrt{S_2}\le \sqrt{S}$ . When equality is reached?