Question 161
Nonnegative real numbers $a$, $b$, $c$ satisfy the equation $a + b + c = 1$. Prove the inequality
$$
(1 - a)^2 + (1 - b)^2 + (1 - c)^2 \geq 6\sqrt{abc}.
$$
Can the case of equality occur?
$$
(1 - a)^2 + (1 - b)^2 + (1 - c)^2 \geq 6\sqrt{abc}.
$$
Can the case of equality occur?