Question

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?

Answer 1

Did you try squaring each side and simplifying?

Answer 2

a^2 + b^2 = (a + b)^2 - 2ab