Problem

Source: ELMO 1999 Problem 3

Tags: inequalities, inequalities unsolved



Prove that \[ 2^6 \frac{abcd+1}{(a+b+c+d)^2} \le a^2+b^2+c^2+d^2+\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}+\frac{1}{d^2} \] for $a,b,c,d > 0$.