若x+y+z=3,且(x≠y≠z≠1),求【(x-1)^2+(y-1)^2+(z-1)^2】/【3(x-1)(y-1)(z-1)】的值.

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若x+y+z=3,且(x≠y≠z≠1),求【(x-1)^2+(y-1)^2+(z-1)^2】/【3(x-1)(y-1)(z-1)】的值.

x十y十z=3
则x-1十y-1十z-1=0
令a=x-1,b=y-1,c=z-1
原式=[(a十b十c)^2-2(ab十bc十ac)]/3abc
=-2/3c-2/3a-2/3b
=-2(c十a十b)/3
=0/3
=0