Question

设m=(|a|-|b|)/|a-b|,n=(|a|+|b|)/|a+b|,则m,n的大小关系是?

Answer 1

计算m^2-n^2

m^2-n^2=(a^2+b^2-2|a||b|)/(a-b)^2- (a^2+b^2+2|a||b|)/(a+b)^2

=1+[2(ab-|a||b|)/(a-b)^2]-1-[2(|a||b|-ab)/(a+b)^2]

=2(ab-|a||b|)/[(a-b)^2*(a+b)^2]

a