and are the geometric mean and the harmonic mean of any two positive (identical or nonidentical) integers. Calculate the minimum value of their arithmetic mean in terms of and .
HM= $\frac {GM^2}{AM}$
AM= $\frac {GM^2}{HM}$
So, AM=$\frac {x^2}{y}$
My conclusion is that minimum value of AM is $\frac{x^2}{y}$.Am I correct?
Yes, given the AM,GM and HM there's no other way to get their relation. So that is the only possible equation to relate the Means.You are correct.