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Question on GP/APs

  1. Jan 8, 2004 #1
    i'm having some trouble with this question on GP/APs. can anybody show me how to do it, and explain? thanks.

    :) J.

    The Culprit:
    Prove that the arithmetic mean of two different positive numbers exceeds the geometric mean of the same two numbers.
     
  2. jcsd
  3. Jan 8, 2004 #2
    Let us take two numbers a and b

    AM= (a+b)/2 = [tex]\frac{(\sqrt{a}-\sqrt{b})^2}{2} + \sqrt{ab}[/tex]

    clearly AM>=GM
     
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