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Triangle Inequality Proof

  1. Sep 24, 2010 #1
    1. The problem statement, all variables and given/known data

    Given:0 <= a <= b

    a <= Sqrt(ab) <= (a+b)/2 <= b

    2. Relevant equations

    3. The attempt at a solution

    The only problem im having prooving this inequality is Sqrt(ab) <= (a+b)/2.
    I have an idea but im not sure if it validates.
    can i do this.. ? (a+b)/2 - sqrt(ab) >= 0
    if it is greater than 0 [ i get an answer of 1/4 (a-b)^2 >= 0 ] , (a+b)/2 must be greater than sqrt(ab). given that
    both sqrt(ab) and (a+b)/2 are >= 0 since 0 < a < b.

    Is my reasoning correct? or wrong
    please help !
  2. jcsd
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