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Suppose that \(|a - b| + |b - c| + |c - a| = 20\). What is the maximum value of \(|a-b|\)

 Jun 28, 2018
 #1
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Let  a  >  c  >  b

 

Then

 

l a - b l  = a  - b

l b - c l  = c - b    and

l c - a l  = a  - c

 

So

 

l a - b l + l b - c l +  l c - a l    = 20      

 

a - b + c - b + a - c  = 20    simplify

 

2a  - 2b  = 20

 

a - b  =10

 

So...the max  value  for   l a - b l    = 10   

 

 

cool cool cool

 Jun 28, 2018

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