Absolute Values and Inequalities

[mentaal]

If x,y,z >0, |x-y|, |y-z|, |x-z| < 2, then [FONT=Verdana, Arial, Helvetica, sans-serif]∑ x <= ∑ sqroot (xy+1).

[/FONT]It's not clear to me how the summation applies to the given inequality and how to tackle it.

[FONT=Verdana, Arial, Helvetica, sans-serif]Not really sure how to get started with this one.. I would appreciate if anyone could give me at least a hint as I am not necessarily interested in a full solution. I would like to understand the procedure! Thanks![/FONT]

 

[stapel]

If x,y,z >0, |x-y|, |y-z|, |x-z| < 2, then ∑ x <= ∑ sqroot (xy+1).

What is the summation over? What are the indices?

Thank you!