Question 115
Prove that
$$
\frac{a+b}{2b+c} + \frac{b+c}{2c+a} + \frac{c+a}{2a+b} \geq 2
$$
is true for any positive real numbers $a, b, c$.
$$
\frac{a+b}{2b+c} + \frac{b+c}{2c+a} + \frac{c+a}{2a+b} \geq 2
$$
is true for any positive real numbers $a, b, c$.