Cho $\triangle ABC$ vuông tại $A$. Cm
a, $(a + b - c)(b + c - a)(c + a - b) \leq abc$
b, $S = 1$ thì $a^{4} + b^{4} + c^{4} \geq 16$
c, $A \geq B \geq C$ thì $\frac{h_{a}}{h_{b}} + \frac{h_{b}}{h_{c}} + \frac{h_{c}}{h_{a}} \geq \frac{h_{b}}{h_{a}} + \frac{h_{a}}{h_{c}} + \frac{h_{c}}{h_{b}}$