Rmo 1993 Here

[ \sqrt(t-2)^2 + \sqrt(t-3)^2 = 1. ] That is ( |t-2| + |t-3| = 1 ), with ( t \ge 0 ).

[ \sqrtx+3-4\sqrtx-1 ;+; \sqrtx+8-6\sqrtx-1 ;=; 1. ] 1. Domain: ( x-1 \ge 0 \Rightarrow x \ge 1 ). rmo 1993

First radical: ( x+3-4\sqrtx-1 = (t^2+1)+3 - 4t = t^2 - 4t + 4 = (t-2)^2 ). [ \sqrt(t-2)^2 + \sqrt(t-3)^2 = 1