Problem

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2009

Tags: System, algebra, minimum, inequalities



Find minimal value of $a \in \mathbb{R}$ such that system $$\sqrt{x-1}+\sqrt{y-1}+\sqrt{z-1}=a-1$$$$\sqrt{x+1}+\sqrt{y+1}+\sqrt{z+1}=a+1$$has solution in set of real numbers