# clarification required for AM GM HM

8 Posts  ·  4 Users
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?
Page 1 of 1 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)

Commenting on this post has been disabled by the moderator. 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
Commenting on this post has been disabled by the moderator. 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

Commenting on this post has been disabled by the moderator. 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
Commenting on this post has been disabled by the moderator. 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
Commenting on this post has been disabled by the moderator. 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...

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?

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.