x²+y²+z²-2x+4y-6z+14=0
x²-2x+y²+4x+z²-6z+1+4+9=0
(x²-2x+1)+(y²+4x+4)+(z²-6z+9)=0
(x-1)²+(y+2)²+(z-3)²=0
则x-1=0,y+2=0,z-3=0
则x=1,y=-2,z=3
则x+y+z=1+(-2)+3=2
x²+y²+z²-2x+4y-6z+14=0
x²-2x+y²+4x+z²-6z+1+4+9=0
(x²-2x+1)+(y²+4x+4)+(z²-6z+9)=0
(x-1)²+(y+2)²+(z-3)²=0
则x-1=0,y+2=0,z-3=0
则x=1,y=-2,z=3
则x+y+z=1+(-2)+3=2