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? hint(s):

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