Question 93
Prove that for positive real a,b,c satisfying abc=1,
$$\frac1{1+a^2+(b+1)^2}+\frac1{1+b^2+(c+1)^2}+\frac1{1+c^2+(a+1)^2}\le\frac12.$$
$$\frac1{1+a^2+(b+1)^2}+\frac1{1+b^2+(c+1)^2}+\frac1{1+c^2+(a+1)^2}\le\frac12.$$
MathNet 2013 Question 93
Math Olympiad Vault · MathNet 2013