If the aritmetic, geometric and harmonic menas between two positive real numbers be A, G and H, then
Let A = a+b2, G =√ab and H = 2aba+b.
Then G2 = ab ..................(i)
and AH = (a+b2).2aba+b = ab ................(ii)
From (i) and (ii), we have G2 = AH