anonymous
  • anonymous
If two numbers have arithmetic mean 2700 and harmonic mean 75, find their geometric mean.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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Jack1
  • Jack1
does that seem correct @vinhu ?
anonymous
  • anonymous
Not quite ! Since the answer is less than 999
Jack1
  • Jack1
might call in the big guns, hang on @Jhannybean and @oldrin.bataku can you guys help...?

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More answers

yrelhan4
  • yrelhan4
let the two numbers be a,b.. arithmetic mean=a+b/2.. geometric mean=sqrt(ab).. two equations, two variables.. find a and b first..
yrelhan4
  • yrelhan4
once you have the two numbers.. (1/a + 1/b)/2 gives you the harmonic mean...
Jack1
  • Jack1
ah, cheers @yrelhan4
yrelhan4
  • yrelhan4
:)
yrelhan4
  • yrelhan4
and.. i should also mention it here, arith mean*geom mean is not equal to harmonic mean.. but for n=2. harmonic mean=G^2/A
Jack1
  • Jack1
we have n=2 here, so doesnt that mean that sqrt (harmonic x Arith) = geometric...?
yrelhan4
  • yrelhan4
geometric^2 on the rhs.
Jack1
  • Jack1
sqrt on the LHS...
yrelhan4
  • yrelhan4
ah, missed it. my bad. yes thats right.
Jack1
  • Jack1
so my initial guess was correct, and we dont have to solve for a and b...?
yrelhan4
  • yrelhan4
no you dont, if you know this formula. but again, the best and the safest thing is to start from the basics.. these formulas are certainly not for beginners.. and i thought you wrote, arith mean*geom=harmonic mean or something like that. sorry about that.
yrelhan4
  • yrelhan4
and i hope @vinhu got it?
Jhannybean
  • Jhannybean
O_o
Jack1
  • Jack1
no, good point, how you get it is important but with this: "once you have the two numbers.. (1/a + 1/b)/2 gives you the harmonic mean..." i think harmonic is n/(1/a + 1/b), so it should be 2 / (1/a + 1/b)... yeah?
yrelhan4
  • yrelhan4
err wth. i am really messing it up today. yes. 1/H=(1/a + 1/b)/2.. so H=2/(1/a + 1/b).
Jack1
  • Jack1
cool, thanks man, i learnt something new just then, cheers @yrelhan4
yrelhan4
  • yrelhan4
I was wrong twice. thanks to you too. :)
anonymous
  • anonymous
Could anyone summarize the point for me since I haven't learned this kind of mathematics before !
yrelhan4
  • yrelhan4
ok look.. arithmetic mean for two numbers= a+b/2 geometric mean= sqrt(ab) harminic mean= 2/(1/a+1/b).. you are given the values of arith and geom mean.. solve those two equations and find the values of a and b.. then put those values in the third equation to get your answer.
anonymous
  • anonymous
I'm still in the middle of nowhere. More detail please!!! My a , b is extremely huge. Also they are decimal numbers !
yrelhan4
  • yrelhan4
Just round them off to up to one decimal points.. and you have all the details you need to solve this.
Jack1
  • Jack1
a= 37.7 ish, b = 5362.2 ish... yeah? @vinhu
Jack1
  • Jack1
all u need so do is solve them like a series of simultaneous equations arithmetic mean for two numbers= a+b/2 2700 = a + b / 2 5400 = a + b so a = 5400 - b plug that into: harmonic mean= 2/(1/a+1/b) 75 = 2/(1/a+1/b) and a = 5400 - b so 75 = 2/(1/(5400 - b)+1/b) solve for b use that to find a use a and b to find geometirc mean ( sqrt (axb))
hartnn
  • hartnn
just an alternate way....might be easier. 5400 = a+b 75= 2ab/ (a+b) = 2ab/ 5400 so, ab = 75*5400/2 = 202500 and Geometric mean is just \(\sqrt{ab}=\sqrt{202500}=450\) see, not much solving was involved :)
hartnn
  • hartnn
and definitely no need to find a and b.

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