+0  
 
0
90
1
avatar+126 

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

 Jun 28, 2018
 #1
avatar+94545 
+2

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

24 Online Users

avatar
avatar
avatar
avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.