若m>n>0,a>0,且a不等于1,比较a∧m+a∧-m与a∧n+a∧-n的大小

A-B=a^m-a^n+1/a^m-1/a^n通分=(a^2m*a^n-a^m*a^2m+a^n-a^m)/a^m*a^n显然分母a^m*a^n>0分子=a^2m*a^n-a^m*a^2m+a^n-a^m=a^m*a^n(a^m-a^n)-(a^m-a^n)=(a^m-a^n)(a^m*a^n-1)若0a^0=1同理a^n>1,所以a^m*a^n>1,a^m*a^n-1>...