Question 53
Suppose $a, b, c$ are the side lengths of a triangle. Prove that
$$
a^2 + b^2 + c^2 \leq a \max(b, c) + b \max(c, a) + c \max(a, b)
$$
with equality iff $a = b = c$.
$$
a^2 + b^2 + c^2 \leq a \max(b, c) + b \max(c, a) + c \max(a, b)
$$
with equality iff $a = b = c$.