Problem

Source: Stars of Mathematics 2020 (junior level)

Tags: algebra, Inequality, romania



Let $a_1,a_2,a_3,a_4$ be positive real numbers satisfying \[\sum_{i<j}a_ia_j=1.\]Prove that \[\sum_{\text{sym}}\frac{a_1a_2}{1+a_3a_4}\geq\frac{6}{7}.\]* * *