设a1,a2……an为正数, ,求证(a1a2)/a3+(a2a3)/a1 +(a3a1)/a2>=a1+a2+a3

问题描述:

设a1,a2……an为正数, ,求证(a1a2)/a3+(a2a3)/a1 +(a3a1)/a2>=a1+a2+a3

因为 a1、a2、a3.都是正数,所以由均值定理得 (a1a2)/a3+(a1a3)/a2>=2*√[a1*a2*a1*a3/(a3*a2)]=2a1 ,同理 (a2a3)/a1+(a2a1)/a3>=2a2 ,(a3a1)/a2+(a3a2)/a1>=2a3 ,将以上三式两边分别相加得2[(a1a2)/a3+(a2a3)/a1 +(a...