ON THE LOWER BOUNDS OF A SYMMETRIC INEQUALITY INVOLVING ROOTS.

In their article in the journal Mathematical Reflections, Campos Daniel and Verdiyan Verdan (2009) proposed an interesting and difficult inequality, which has appeared on several occasions in the MathLinks forum (http://www.artofproblemsolving.com/Forum/index.php), without any references to its solution. In this paper, we present two original solutions to this inequality problem. We also consider various generalizations of this inequality from various perspectives. Finally, we apply the general results to solve some other difficult inequalities. [ABSTRACT FROM AUTHOR]