AM-GM-HM Relationship
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
asked Nov 17 at 17:06
CreamPie
255
add a comment |
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
asked Nov 17 at 17:06
CreamPie
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
add a comment |
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
asked Nov 17 at 17:06
CreamPie
255
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
asked Nov 17 at 17:06
CreamPie
255
asked Nov 17 at 17:06
CreamPie
255
asked Nov 17 at 17:06
CreamPie
255
asked Nov 17 at 17:06
CreamPie
255
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
add a comment |
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
add a comment |
1 Answer
1
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.
answered Nov 20 at 14:27
PiGuy
1487
add a comment |
1 Answer
1
active
oldest
votes
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.
answered Nov 20 at 14:27
PiGuy
1487
add a comment |
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.
answered Nov 20 at 14:27
PiGuy
1487
add a comment |
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.
answered Nov 20 at 14:27
PiGuy
1487
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.
answered Nov 20 at 14:27
PiGuy
1487
answered Nov 20 at 14:27
PiGuy
1487
answered Nov 20 at 14:27
PiGuy
1487
answered Nov 20 at 14:27
PiGuy
1487
1487
add a comment |
add a comment |
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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