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Suppose that \(|a - b| + |b - c| + |c - a| = 20\)

What is the maximum possible value of \(|a-b|\)?

 Apr 14, 2019
 #1
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l a - b l  will be maximized when a is large as possible and b is as small as possible

 

So....suppose that   a > c > b

 

Then we have that

 

(a - b) +( c - b) + ( a - c)  = 20

 

2a - 2b  =  20            divide through by 2

 

a - b  =  10

 

So

 

l a - b l  =  10

 

 

cool cool cool

 Apr 14, 2019

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