Problem

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 (aixbi)22005ji,j=1(ajxbj) for all real numbers x and every integer i with 1i2005. What is maximal number of positive ai's and bi's?