Let a1,a2,...,a2005,b1,b2,...,b2005 be real numbers such that (aix−bi)2≥∑2005j≠i,j=1(ajx−bj) for all real numbers x and every integer i with 1≤i≤2005. What is maximal number of positive ai's and bi's?
Source: 2006 MOP Homework Blue Algebra 5
Tags: inequalities, algebra, Sum, Maximal, max
Let a1,a2,...,a2005,b1,b2,...,b2005 be real numbers such that (aix−bi)2≥∑2005j≠i,j=1(ajx−bj) for all real numbers x and every integer i with 1≤i≤2005. What is maximal number of positive ai's and bi's?