Mathematics RELATION BETWEEN AM AND GM

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RELATION BETWEEN AM AND GM

Relation between `A.M.` and `G.M.` : `A.M. ge G.M`

Let `A` and `G` be the `AM` and `GM ` between two positive numbers `a` and `b` then `A ge G`

(Sign of equality holds when `a= b` )

`A.M` between `a` & `b, A=(a+b)/2`

`GM` between `a` & `b, G =sqrt(ab)`

`A-G=(a+b)/2-sqrt(ab)=1/2(sqrt a-sqrt b)^2`

`=> A-G >0=>A ge G`

(lf `a = b` then `A- G =0` `=>A=G`)

then `A.M. ge G.M`