Let \(a,b,c,d\) be positive real numbers such that \(a+b+c+d=1\) Find the minimum value of
\(\frac{a}{b + c + d} + \frac{b}{a + c + d} + \frac{c}{a + b + d} + \frac{d}{a + b + c}.\)
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.
+159 
