We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
130
1
avatar+133 

Let   \(a,b,c,d\)  be positive real numbers such that \(a+b+c+d=1\) Find the minimum value of

 

\(\frac{a}{b + c + d} + \frac{b}{a + c + d} + \frac{c}{a + b + d} + \frac{d}{a + b + c}.\)
 

 Aug 3, 2019
 #1
avatar+6045 
+1

using Lagrange multipliers you can show that the minimum occurs when a=b=c=d=1/4 and is equal to 4/3

 

but you can also argue this from symmetry since they are all required to be positive.

 Aug 3, 2019

7 Online Users

avatar
avatar
avatar