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Relationship Between A.M. and G.M.

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  • Relation Between Arithematic Mean (A.M.) and Geometric Mean (G.M.)

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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`.

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