Prove thata2+b2−2ab+b2+c2−2bc≥a2+c2 \sqrt{a^2 + b^2 - \sqrt{2} ab} + \sqrt{b^2 + c^2 - \sqrt{2} bc} \geq \sqrt{a^2 + c^2} a2+b2−2ab+b2+c2−2bc≥a2+c2for all positive real numbers aaa, bbb and ccc.
