已知f(x)=(1/2)x,a,b∈R+,A=f(A+B)/2,G=f根号ab...则AGH的大小关系是?

Question

已知f(x)=(1/2)x,a,b∈R+ ,A=f(A+B)/2,G=f根号ab...则AGH的大小关系是?

Answer 1

(a+b)²≥4ab
(a+b)/4≥ab
(a+b)/2≥2ab/(a+b)
(a+b)≥2√ab
(a+b)/2≥√ab
(√ab)(a+b)≥2ab
√ab≥2ab/(a+b)
(a+b)/2≥√ab≥2ab/(a+b)>0
A