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3

Part of 2011 239 Open Mathematical Olympiad

Problems(1)

a+b+c+d=4, prove sum_{cyc}\frac{a}{a^3 + 4} < 4/5

Source: 239 2011 S3

5/19/2020
Positive reals a,b,c,da,b,c,d satisfy a+b+c+d=4a+b+c+d=4. Prove that ∑cycaa3+4≤45\sum_{cyc}\frac{a}{a^3 + 4} \le \frac{4}{5}
inequalities