Question 6
Prove that
$$
3abc + a + b + c \ge 2(ab + bc + ca)
$$
holds for all real numbers $a, b, c \ge 1$.
Determine all cases for which the equality is obtained.
$$
3abc + a + b + c \ge 2(ab + bc + ca)
$$
holds for all real numbers $a, b, c \ge 1$.
Determine all cases for which the equality is obtained.