Question 60
Let $a, b, c$ be non-negative real numbers such that $a+b \le c+1$, $b+c \le a+1$ and $c+a \le b+1$. Prove that
$$
a^2 + b^2 + c^2 \le 2abc + 1.
$$
$$
a^2 + b^2 + c^2 \le 2abc + 1.
$$
MathNet 2007-part-02 — 187 problems (EN–VI) Question 60
Math Olympiad Vault · MathNet 2007-part-02 — 187 problems (EN–VI)