设A.B.C均为正数,求证c/(a+b)+a/(b+c)+b/(c+a)>=3/2

问题描述:

设A.B.C均为正数,求证c/(a+b)+a/(b+c)+b/(c+a)>=3/2

左边 =(a+b+c)/(a+b)+(a+b+c)/(b+c)+(a+b+c)/(c+a)-3 =0.5×(a+b+b+c+c+a)*[1/(a+b)+1/(b+c)+1/(c+a)]-3 ≥0.5×{3×[(a+b)(b+c)(c+a)]^1/3}×{3×[1/(a+b)×1/(b+c)×1/(c+a)]^1/3}-3 =0.5×3×3-3 =3/2 所以c/...