Question 138
Let $a, b, c$ be positive numbers such that $a^{2}+b^{2}+c^{2}+a b c=4$. Prove that
$$
\frac{a+b}{c}+\frac{b+c}{a}+\frac{c+a}{b} \geq a+b+c+\frac{1}{a}+\frac{1}{b}+\frac{1}{c} .
$$
$$
\frac{a+b}{c}+\frac{b+c}{a}+\frac{c+a}{b} \geq a+b+c+\frac{1}{a}+\frac{1}{b}+\frac{1}{c} .
$$