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Question about relation between powers and distance

  1. May 2, 2012 #1
    I have this formula:

    (x+α)(x+α)*(y+β)(y+β)*(z+γ)(z+γ)=xx*yy*zz

    where α+β+γ=0

    I think there might be a distance relationship between x, y and z that would satisfy the equation: if x,y and z are varied with keeping a certain measure of distance constant, the equation will be verified. This is a presupposition of mine I would like to prove or disprove, but I don't know where to start.

    Do you have any ideas?

    Thank you.
     
  2. jcsd
  3. May 2, 2012 #2

    chiro

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    Science Advisor

    Hey arthurav and welcome to the forums.

    One suggestion I have is to take logs of both sides and then take it from there. You should get things in terms of xlog(x) + ylog(y) + zlog(z) = (x+a)log(x+a) + (y+b)log(y+b) + (z+c)log(z+c).

    Also, in addition this might help: http://www.arts.cornell.edu/econ/arazin/loglinearization.pdf [Broken]
     
    Last edited by a moderator: May 6, 2017
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