MathNet 2007-part-03 — 185 problems (EN–VI) Question 39

Prove that $$\sqrt{a^2 + b^2 - \sqrt{2} ab} + \sqrt{b^2 + c^2 - \sqrt{2} bc} \geq \sqrt{a^2 + c^2}$$ for all positive real numbers $a$, $b$ and $c$.