由算术平方根的意义知:x+y-2002≥0且2002-x-y≥0
解之,得:x+y=2002
于是,根号3x+y-z-2 +根号2x+y-z = 0
可得:3x+y-z-2=0且2x+y-z = 0
故,x=2, y=2000, z=2004.