Question 4
I 4 (USS 4)
The sum of the squares of five real numbers $a_1,a_2,a_3,a_4,a_5$ equals $1$. Prove that the least of the numbers $(a_i-a_j)^2$, where $i,j=1,2,3,4,5$ and $i\ne j$, does not exceed $1/10$.
The sum of the squares of five real numbers $a_1,a_2,a_3,a_4,a_5$ equals $1$. Prove that the least of the numbers $(a_i-a_j)^2$, where $i,j=1,2,3,4,5$ and $i\ne j$, does not exceed $1/10$.