∵x^2+y^2+z^2-2x+4y-6z+14
= x^2+y^2+z^2-2x+4y-6z++1+4+9
=(x²-2x+1)+(y²+4y+4)+(z²-6z+9)
=(x-1)²+(y+2)²+(z-3)²
=0
又∵(x-1)²≥0,(y+2)²≥0,(z-3)²≥0
∴三个非负数之和为0,则这三个非负数都为0
即x-1=0,y+2=0,z-3=0
解得：x=1,y=-2,z=3
即x+y+z=1-2+3=2
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