实数a,b,m,n满足a

题目

实数a,b,m,n满足a

答案

M-N=（a+mb)/(1+m)-(a+nb)/(1+n)
=[(a+mb)(1+n)-(a+nb)(1+m)]/(1+m)(1+n)
=[(a+an+mb+mnb)-(a+am+nb+mnb)]/(1+m)(1+n)
=(an-am+mb-nb)/(1+m)(1+n)
=(b-a)(m-n)/(1+m)(1+n)
>0
所以,M>N