(adsbygoogle = window.adsbygoogle || []).push({}); 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.

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# Homework Help: Show max(a,b) = (a + b + |a-b|)+2

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