MathDB
find x_i, i=1,2,3 if Σx_i+Σ3/(x_i-1)-2Σ\sqrt{x_i+2}=0

Source: Nordic Mathematical Contest 1992 #1

October 5, 2017
algebraequation

Problem Statement

Determine all real numbers x>1,y>1x > 1, y > 1, and z>1z > 1,satisfying the equation x+y+z+3x−1+3y−1+3z−1=2(x+2+y+2+z+2)x+y+z+\frac{3}{x-1}+\frac{3}{y-1}+\frac{3}{z-1}=2(\sqrt{x+2}+\sqrt{y+2}+\sqrt{z+2})
Back to ProblemsView on AoPS