Question 45
Let $a, b, c$ be real numbers such that $0 \le a \le b \le c$. Prove that if
$$
a + b + c = ab + bc + ca \gt 0,
$$
then $\sqrt{bc}(a + 1) \ge 2$. When does the equality hold?
$$
a + b + c = ab + bc + ca \gt 0,
$$
then $\sqrt{bc}(a + 1) \ge 2$. When does the equality hold?