Question 3
Prove that
$$
\left(a^{2}+2\right)\left(b^{2}+2\right)\left(c^{2}+2\right) \geq 9(ab+bc+ca)
$$
for all real numbers $a, b, c \gt 0$.
$$
\left(a^{2}+2\right)\left(b^{2}+2\right)\left(c^{2}+2\right) \geq 9(ab+bc+ca)
$$
for all real numbers $a, b, c \gt 0$.