Question 44
Prove that if $x, y, z \in \mathbb{R}$, then the following inequality holds:
$$
\sum_{\text{cyc}} \sqrt{1 + (x\sqrt{1+y^2} + y\sqrt{1+x^2})^2} \geq xy + yz + zx + 2(x+y+z).
$$
$$
\sum_{\text{cyc}} \sqrt{1 + (x\sqrt{1+y^2} + y\sqrt{1+x^2})^2} \geq xy + yz + zx + 2(x+y+z).
$$