Question 67
Let $a, b, c \in [0, 1]$. Prove that
$$
\frac{1}{1+a+b} + \frac{1}{1+b+c} + \frac{1}{1+c+a} + a+b+c \le 3 + \frac{1}{3}(ab+bc+ca).
$$
$$
\frac{1}{1+a+b} + \frac{1}{1+b+c} + \frac{1}{1+c+a} + a+b+c \le 3 + \frac{1}{3}(ab+bc+ca).
$$
MathNet 2012 Question 67
Math Olympiad Vault · MathNet 2012