Question 46
For real numbers $a$, $b$, $c$, prove that
$$
a^2 + b^2 + c^2 + \frac{2ab}{1 + |a - b|} \geq \frac{2bc}{1 + |b + c|} + \frac{2ca}{1 + |c + a|}.
$$
$$
a^2 + b^2 + c^2 + \frac{2ab}{1 + |a - b|} \geq \frac{2bc}{1 + |b + c|} + \frac{2ca}{1 + |c + a|}.
$$