China Girls' Mathematical Olympiad

Let $△ABC$ be a triangle. Points $D$ and $E$ are on sides $AB$ and $AC$, respectively, and point $F$ is on line segment $DE$. Let $\frac{AD}{AB}=x$, $\frac{AE}{AC}=y$, $\frac{DF}{DE}=z$. Prove that

(1) $S_{△BDF}=(1-x)yz{S}_{△ABC}$ and $S_{△CEF}=x(1-y)(1-z)S_{△ABC}$;

(2) $\sqrt[3]{S_{△BDF}}+\sqrt[3]{S_{△CEF}}\le \sqrt[3]{S_{△ABC}}$.

(posed by Li Weigu)