Question 2
Let $a$, $b$ and $c$ be the sides of a triangle and $p = a + b + c$. Show that
a. $\frac{a}{b+c-a} + \frac{b}{c+a-b} + \frac{c}{a+b-c} \ge 3$;
b. $a^k + b^k \gt \frac{c^k}{2^{k-1}}$ for $k = 2, 3, 4, \dots$;
c. $a^k + b^k + c^k \ge \frac{p^k}{3^{k-1}}$ for $k = 2, 3, 4, \dots$.
a. $\frac{a}{b+c-a} + \frac{b}{c+a-b} + \frac{c}{a+b-c} \ge 3$;
b. $a^k + b^k \gt \frac{c^k}{2^{k-1}}$ for $k = 2, 3, 4, \dots$;
c. $a^k + b^k + c^k \ge \frac{p^k}{3^{k-1}}$ for $k = 2, 3, 4, \dots$.