已知 x+y+z=3 求证(x-1)^3+(y-1)^3+(z-1)^3-3(x-1)(y-1)(z-1)=0
问题描述：
已知 x+y+z=3 求证(x-1)^3+(y-1)^3+(z-1)^3-3(x-1)(y-1)(z-1)=0
答
由x+y+z=3可知（x-1）+（y-1）+（z-1）=0.令x-1=ay-1=bz-1=c0=a+b+cc=-(a+b)(x-1)^3+(y-1)^3+(z-1)^3-3(x-1)(y-1)(z-1)=a^3+b^3-(a+b)^3-3abc=a^3+b^3-(a^3+3a^2b+3ab^2+b^3)-3abc=-3a^2b-3ab^2-3abc=-3ab(a+b+c)=-3...