Problem

Source: Indonesian TST for IMO 2023 Stage 1: Test 2 - Algebra

Tags: algebra, inequalities proposed, Indonesia, Indonesia TST



Let $a,b,c$ positive real numbers and $a+b+c = 1$. Prove that \[a^2 + b^2 + c^2 + \frac{3}{\frac{1}{a} + \frac{1}{b} + \frac{1}{c}} \ge 2(ab + bc + ac)\]