1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Show max(a,b) = (a + b + |a-b|)+2

  1. Sep 22, 2008 #1
    1. The problem statement, all variables and given/known data
    let a and b be two real numbers show that max{a,b} = (a + b + |a - b|)/2


    2. Relevant equations
    I have all the field properties of the real numbers and order, LUB and existence of square root.

    I also have definition of absolute value.


    3. The attempt at a solution
    This is very easy for me to see on the real line. If I break it into (a+b)/2 + |a+b|/2 then it is clear that I am taking the midpoint and adding half the distance between a and b.

    However I am not sure I should argue it that way. I think that I should somehow be using my LUB properties but I don't know how.

    Any help is appreciated.
     
  2. jcsd
  3. Sep 22, 2008 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Re: Max

    Split it into the two cases a>=b and a<b?
     
  4. Sep 23, 2008 #3
    Re: Max

    I did think about doing it that way, but I think within each of those cases there will be 3 others as well.

    So assume a < b, then I have to consider if a and b are positive, if a and b are negative and if a is negative b is positive.

    And all I really know by assuming a < b is that b - a > 0. Which I can't seem to make a connection to the formula (a + b + |a-b|)/2.
     
  5. Sep 23, 2008 #4

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Re: Max

    If a<b then i) max(a,b)=b and ii) a-b<0, so |a-b|=-(a-b). Can you check it works now?
     
  6. Sep 23, 2008 #5
    Re: Max

    Thanks so much
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?