Question 49
Prove that for all real numbers $a, b, c$ the following inequality holds
$$
\frac{1}{3}(a+b+c)^2 \leq a^2 + b^2 + c^2 + 2(a-b+1).
$$
$$
\frac{1}{3}(a+b+c)^2 \leq a^2 + b^2 + c^2 + 2(a-b+1).
$$
MathNet 2012 Question 49
Math Olympiad Vault · MathNet 2012