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Homework Help: Help with a proof.

  1. Feb 8, 2010 #1
    1. The problem statement, all variables and given/known data
    Prove max (a,b) = [tex]\frac{a+b + \left|a+b\right|}{2}[/tex]

    Make 3 cases:

    Case 1: Assume a > b. Show both sides come out with the same number.
    Case 2: Assume a < b. Show both sides come out with the same number.
    Case 3: Assume a = b. Show both sides come out with the same number.


    2. Relevant equations
    N/A


    3. The attempt at a solution

    To be honest I'm not sure how to set up both sides to begin with before I even start to break it down to address each case. Once I see how to do that I should be able to be able to prove this.
     
  2. jcsd
  3. Feb 8, 2010 #2

    statdad

    User Avatar
    Homework Helper

    First make sure you have the correct statement: if you check your expression for a = 5, b = 10, you get

    [tex]
    \frac{5+10 + |5+10|}{2} = \frac{15 + 15} 2 = 15
    [/tex]

    which is not the maximum of the numbers 5 and 10. Perhaps it should be

    [tex]
    \max(a,b) = \frac{(a+b) + |a-b|}{2}
    [/tex]

    Consider your final case: if [tex] a = b [/tex], what can you say about which one is the maximum? Then, what can you say about how the right-side simplifies if the two inputs are equal?
     
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