MathDB

6

Part of 2013 USAJMO

Problems(1)

Square Root Equality

Source: 2013 USAJMO #6/USAMO #4

5/1/2013
Find all real numbers x,y,z≥1x,y,z\geq 1 satisfying min⁡(x+xyz,y+xyz,z+xyz)=x−1+y−1+z−1.\min(\sqrt{x+xyz},\sqrt{y+xyz},\sqrt{z+xyz})=\sqrt{x-1}+\sqrt{y-1}+\sqrt{z-1}.
AMCUSA(J)MOUSAJMOparameterizationinequalities