In a triangle $A B C$, consider points $D$ and $E$ on $A C$ and $A B$, respectively, and assume that they do not coincide with any of the vertices $A , B , C$. If the segments $B D$ and $C E$ intersect at $F$, consider the areas $w , x , y , z$ of the quadrilateral $A E F D$ and the triangles $B E F , B F C , C D F$, respectively.
(a) Prove that $y ^ { 2 } > x z$.
(b) Determine $w$ in terms of $x , y , z$.