ELMO 1999 Problem 3

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 $a,b,c,d > 0$ .

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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