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A1

Part of 2013 Balkan MO Shortlist

Problems(1)

1/(4+(a+b)^2)+1/(4+(b+c)^2)+1/(4+(c+a)^2)<= 3/8 for ab + bc+ ca = 3

Source: Balkan MO Shortlist 2013 A1 BMO

3/8/2020
Positive real numbers a,b,ca, b,c satisfy ab+bc+ca=3ab + bc+ ca = 3. Prove the inequality 14+(a+b)2+14+(b+c)2+14+(c+a)2≤38\frac{1}{4+(a+b)^2}+\frac{1}{4+(b+c)^2}+\frac{1}{4+(c+a)^2}\le \frac{3}{8}
inequalitiesalgebra