Question 3
Let $x,y,z\gt 0$ satisfy
$$\frac1x+\frac1y+\frac1z\lt \frac1{xyz}.$$
Show that
$$\frac{2x}{\sqrt{1+x^2}}+\frac{2y}{\sqrt{1+y^2}}+\frac{2z}{\sqrt{1+z^2}}\lt 3.$$
$$\frac1x+\frac1y+\frac1z\lt \frac1{xyz}.$$
Show that
$$\frac{2x}{\sqrt{1+x^2}}+\frac{2y}{\sqrt{1+y^2}}+\frac{2z}{\sqrt{1+z^2}}\lt 3.$$