Question 12
Suppose $p \ge 1$ and $a$, $b$, $c$ are the side lengths of a triangle. Prove that
$$
2(a^p + b^p + c^p) \lt (a+b+c)(a^{p-1} + b^{p-1} + c^{p-1}) \le 3(a^p + b^p + c^p).
$$
$$
2(a^p + b^p + c^p) \lt (a+b+c)(a^{p-1} + b^{p-1} + c^{p-1}) \le 3(a^p + b^p + c^p).
$$