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Let a, b, and c be positive real numbers. Prove that

$$\sqrt{a^2 - ab + b^2} + \sqrt{a^2 - ac + c^2} \ge \sqrt{b^2 + bc + c^2}.$$

Under what conditions does equality occur? That is, for what values of a, b, and c are the two sides equal?

Jul 21, 2021