Question 164
Let $a, b$, and $c$ be nonnegative real numbers such that
$$
a^2 + b^2 + c^2 + abc = 4.
$$
Prove that
$$
0 \le ab + bc + ca - abc \le 2.
$$
$$
a^2 + b^2 + c^2 + abc = 4.
$$
Prove that
$$
0 \le ab + bc + ca - abc \le 2.
$$
MathNet 2001 — Part 01 Question 164
Math Olympiad Vault · MathNet 2001 — Part 01