设x,y,z是实数,且(x-y)^2+(y-z)^2+(z-x)^2=(x+y-2z)^2+(y+z-2x)^2+(z+x-2y)^2求[(xy+1)(yz+1)(zx+1)]/

(x+y-2z)^2+(y+z-2x)^2+(z+x-2y)^2=((x-z)+(y-z))²+((y-x)+(z-x))²+((z-y)+(x-y))²=(x-z)²+(y-z)²+2(x-z)(y-z)+(y-x)²+(z-x)²+2(y-x)(z-x)+(z-y)²+(x-y)²+2(z-y)(x-y)...