# Homework Help: Help with a proof.

1. Feb 8, 2010

### The_Iceflash

1. The problem statement, all variables and given/known data
Prove max (a,b) = $$\frac{a+b + \left|a+b\right|}{2}$$

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. Feb 8, 2010

$$\frac{5+10 + |5+10|}{2} = \frac{15 + 15} 2 = 15$$
$$\max(a,b) = \frac{(a+b) + |a-b|}{2}$$
Consider your final case: if $$a = b$$, 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?