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Question Number 1268 by 314159 last updated on 18/Jul/15
Prove that AM > HM.
ProvethatAM>HM.
Answered by prakash jain last updated on 18/Jul/15
AM=((a+b)/2), HM=((2ab)/(a+b)) AM−HM=((a+b)/2)−((2ab)/(a+b))= (((a−b)^2 )/(2(a+b))) If a,b>0 then AM≥HM AM ≥HM is only valid for +ve numbers. Try: a=−4, b=2
AM=a+b2,HM=2aba+bAM−HM=a+b2−2aba+b=(a−b)22(a+b)Ifa,b>0thenAM⩾HMAM⩾HMisonlyvalidfor+venumbers.Try:a=−4,b=2

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