Problem

Source: 2013 USAJMO #6/USAMO #4

Tags: AMC, USA(J)MO, USAJMO, parameterization, inequalities



Find all real numbers $x,y,z\geq 1$ satisfying \[\min(\sqrt{x+xyz},\sqrt{y+xyz},\sqrt{z+xyz})=\sqrt{x-1}+\sqrt{y-1}+\sqrt{z-1}.\]