A Triangle Inequality via Substitution

Problem

Let $a, b, c$ be the side lengths of a triangle. Prove that

a^2\left(\frac{b}{c} - 1\right) + b^2\left(\frac{c}{a} - 1\right) + c^2\left(\frac{a}{b} - 1\right) \;\ge\; 0.

Answer

Solution

Difficulty	7/10
Topics	AM-GM, inequality

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