Problem 6 a1,a2,…,an>0a_1,a_2,\dots ,a_n>0a1,a2,…,an>0 are positive real numbers such that ∑i=1n1ai=n\sum_{i=1}^{n} \frac{1}{a_i}=n∑i=1nai1=n prove that: ∑i<j(ai−ajai+aj)2≤n22(1−n∑i=1nai)\sum_{i<j} \left(\frac{a_i-a_j}{a_i+a_j}\right)^2\le\frac{n^2}{2}\left(1-\frac{n}{\sum_{i=1}^{n}a_i}\right)∑i<j(ai+ajai−aj)2≤2n2(1−∑i=1nain)