Question

若正数k是实数2a,2b的等差中项,根号K是a,b的等比中项,则K的取值范围是?

Answer 1

易知

k=a+b,k=ab,a+b=ab,且a,b同号,a和b均不为1,均不为0.

b=a/(a-1),

k=ab=a^2/(a-1)=(u+1)^2/u=2+u+1/u,u=a-1>0

所以k>=4