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a\sqrt{b^2+c^2+bc}+b\sqrt{c^2+a^2+ca}+c\sqrt{a^2+b^2+ab}>= \sqrt3

Source: 2013 Saudi Arabia BMO TST II p6

July 24, 2020
algebrainequalities

Problem Statement

Let a,b,ca, b,c be positive real numbers such that ab+bc+ca=1ab + bc + ca = 1. Prove that ab2+c2+bc+bc2+a2+ca+ca2+b2+ab≥3a\sqrt{b^2 + c^2 + bc} + b\sqrt{c^2 + a^2 + ca} + c\sqrt{a^2 + b^2 + ab} \ge \sqrt3
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