Question 150
If $a, b, c \in [-1, 1]$ satisfy $a + b + c + abc = 0$, prove that
$$
a^2 + b^2 + c^2 \ge 3(a + b + c).
$$
When does the equality hold?
$$
a^2 + b^2 + c^2 \ge 3(a + b + c).
$$
When does the equality hold?
MathNet 2017-part-04 — 176 problems (EN–VI) Question 150
Math Olympiad Vault · MathNet 2017-part-04 — 176 problems (EN–VI)