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?
By the Cosine Law, a^2 - ab + b^2 = c^2 cos C. Plug in similar expressions, and the rest is easy.
