- Relation Between Arithematic Mean (A.M.) and Geometric Mean (G.M.)
Let A and G be A.M. and G.M. of two given positive real numbers a and b, respectively. Then
A = `(a+b)/2` and G =` sqrt (ab)`
thus , we have
A -G = `(a+b)/2 - sqrt (ab) = (a+b-2 sqrt (ab))/2`
=`(sqrt a -sqrt b)^2/2 >=0` ...(1)
From(1) , we obtain the relationship `A >= G`.