已知x+y+z=3(x,y,z不同时为1),求(x-1)(y-1)(z-1)/(x-1)^3+(y-1)^3+(z-1)^3

Question

已知x+y+z=3(x,y,z不同时为1),求(x-1)(y-1)(z-1) /(x-1)^3+(y-1)^3+(z-1)^3

Answer 1

x=0 y=1 z=2
…
(x-1)(y-1)(z-1)/(x-1)^3+(y-1)^3+(z-1)^3=0