clarification required for AM GM HM

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guys, we have an inequality relation for numbers given by AM >= GM >= HM now my doubt is that when does this inequality hold i mean what type (real, positive, integers etc..) should x y be so that i can use this inequality?
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One thing for sure - U CANT use it for negative values..... for e.g consider GM of two numbers such that one of them is negative, Their GM would be imaginary in that case. So i think this property i.e. AM>GM>HM holds for only positive real nos. (not sure though)

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see, what you're saying is a very general statement....

e.g even -4, -1, 2 forms an AP with common difference = 3

but in this case, AM = -1 whereas GM = 2 and clearly here AM

I dont think it is possible to consider for more than 2 entries. That is if u take any two integers, then AM = a+b /2 , GM = sqrt (a*b) and HM = 2ab/(a+b) where a and b are only positive. Consider 2/3 and 4/5, The AM = 0.73333, GM = 0.7302 and HM = 0.7272
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see, what you're saying is a very general statement....

e.g even -4, -1, 2 forms an AP with common difference = 3

but in this case, AM = -1 whereas GM = 2 and clearly here AM

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msksent Says
Yes anything which u can express in the form of a series. Eg. If 2 and 5 are the terms of an AP, then AM = 3.5, GM = sqrt(10) = 3.1 and HM = 3.27. Try yourself with own examples

I made a mistake HM = 20/7 = 2.86 and hence AM > GM> HM
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yes thats true.. can use it for integers, but what else..?

i do know that i holds for positive fractions as well

seems like a very elementary doubt, maybe too elementary for anyone to reply to...

Yes anything which u can express in the form of a series. Eg. If 2 and 5 are the terms of an AP, then AM = 3.5, GM = sqrt(10) = 3.1 and HM = 3.27. Try yourself with own examples
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yes thats true.. can use it for integers, but what else..?

i do know that i holds for positive fractions as well

seems like a very elementary doubt, maybe too elementary for anyone to reply to...

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guys,

we have an inequality relation for numbers given by

AM >= GM >= HM

now my doubt is that when does this inequality hold i mean what type (real, positive, integers etc..) should x y be so that i can use this inequality?

For any integers, u can use.
Commenting on this post has been disabled by the moderator.

guys,

we have an inequality relation for numbers given by

AM >= GM >= HM

now my doubt is that when does this inequality hold i mean what type (real, positive, integers etc..) should x y be so that i can use this inequality?

Commenting on this post has been disabled by the moderator.