AM-GM-HM Relationship











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𝑥 and 𝑦 are the geometric mean and the harmonic mean of any two positive (identical or nonidentical)
integers. Calculate the minimum value of their arithmetic mean in terms of 𝑥 and 𝑦.



HM= $frac {GM^2}{AM}$



AM= $frac {GM^2}{HM}$



So, AM=$frac {x^2}{y}$



My conclusion is that minimum value of AM is $frac{x^2}{y}$.Am I correct?






sequences-and-series arithmetic means







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  • Somebody help please
    – CreamPie
    Nov 17 at 18:11






  • 1




    mention anything if you find it doesn't help you
    – PiGuy
    Nov 20 at 14:58










  • @PiGuy It was helpful
    – CreamPie
    Nov 20 at 15:21















up vote
1
down vote

favorite












𝑥 and 𝑦 are the geometric mean and the harmonic mean of any two positive (identical or nonidentical)
integers. Calculate the minimum value of their arithmetic mean in terms of 𝑥 and 𝑦.



HM= $frac {GM^2}{AM}$



AM= $frac {GM^2}{HM}$



So, AM=$frac {x^2}{y}$



My conclusion is that minimum value of AM is $frac{x^2}{y}$.Am I correct?






sequences-and-series arithmetic means







share|cite|improve this question






















  • Somebody help please
    – CreamPie
    Nov 17 at 18:11






  • 1




    mention anything if you find it doesn't help you
    – PiGuy
    Nov 20 at 14:58










  • @PiGuy It was helpful
    – CreamPie
    Nov 20 at 15:21













up vote
1
down vote

favorite









up vote
1
down vote

favorite











𝑥 and 𝑦 are the geometric mean and the harmonic mean of any two positive (identical or nonidentical)
integers. Calculate the minimum value of their arithmetic mean in terms of 𝑥 and 𝑦.



HM= $frac {GM^2}{AM}$



AM= $frac {GM^2}{HM}$



So, AM=$frac {x^2}{y}$



My conclusion is that minimum value of AM is $frac{x^2}{y}$.Am I correct?






sequences-and-series arithmetic means







share|cite|improve this question













𝑥 and 𝑦 are the geometric mean and the harmonic mean of any two positive (identical or nonidentical)
integers. Calculate the minimum value of their arithmetic mean in terms of 𝑥 and 𝑦.



HM= $frac {GM^2}{AM}$



AM= $frac {GM^2}{HM}$



So, AM=$frac {x^2}{y}$



My conclusion is that minimum value of AM is $frac{x^2}{y}$.Am I correct?






sequences-and-series arithmetic means




sequences-and-series arithmetic means






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Nov 17 at 17:06









CreamPie

255




255












  • Somebody help please
    – CreamPie
    Nov 17 at 18:11






  • 1




    mention anything if you find it doesn't help you
    – PiGuy
    Nov 20 at 14:58










  • @PiGuy It was helpful
    – CreamPie
    Nov 20 at 15:21


















  • Somebody help please
    – CreamPie
    Nov 17 at 18:11






  • 1




    mention anything if you find it doesn't help you
    – PiGuy
    Nov 20 at 14:58










  • @PiGuy It was helpful
    – CreamPie
    Nov 20 at 15:21
















Somebody help please
– CreamPie
Nov 17 at 18:11




Somebody help please
– CreamPie
Nov 17 at 18:11




1




1




mention anything if you find it doesn't help you
– PiGuy
Nov 20 at 14:58




mention anything if you find it doesn't help you
– PiGuy
Nov 20 at 14:58












@PiGuy It was helpful
– CreamPie
Nov 20 at 15:21




@PiGuy It was helpful
– CreamPie
Nov 20 at 15:21










1 Answer
1






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Yes, given the AM,GM and HM there's no other way to get their relation. So that is the only possible equation to relate the Means.You are correct.






share|cite|improve this answer





















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    1 Answer
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    active

    oldest

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    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes








    up vote
    1
    down vote



    accepted










    Yes, given the AM,GM and HM there's no other way to get their relation. So that is the only possible equation to relate the Means.You are correct.






    share|cite|improve this answer

























      up vote
      1
      down vote



      accepted










      Yes, given the AM,GM and HM there's no other way to get their relation. So that is the only possible equation to relate the Means.You are correct.






      share|cite|improve this answer























        up vote
        1
        down vote



        accepted







        up vote
        1
        down vote



        accepted






        Yes, given the AM,GM and HM there's no other way to get their relation. So that is the only possible equation to relate the Means.You are correct.






        share|cite|improve this answer












        Yes, given the AM,GM and HM there's no other way to get their relation. So that is the only possible equation to relate the Means.You are correct.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Nov 20 at 14:27









        PiGuy

        1487




        1487






























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