2（根号x+根号（y-1）+根号（z-2）=x+y+zx-2根号x+y-2根号（y-1）+z-2根号（z-2）=0(x-2根号x+1)+[y-1-2根号（y-1）+1]+[z-2-2根号（z-2）+1]=0（根号x-1)^2+[根号（y-1）-1]^2+[根号（z-2）-1]^2=0所以x=1，y=2，z=3所以xyz=6
