Question

试证明(x+y-2z)+(y+z-2x)+(z+x-2y)=3(x+y-2z)(y+z-2x)(z+x-2y)

Answer 1

有这样的公式：a^3+b^3+c^2-3abc=(a+b+c)(a^2+b^2+c^2-ab-bc-ca) 左边减右边,证明：（x+y-2z)^3+(y+z-2x)^3+(z+x-2y)^3-3（x+y-2z)(y+z-2x)(z+x-2y) =[（x+y-2z)+(y+z-2x)+(z+x-2y)][（x+y-2z)^2+(y+z-2x)^2+(z+x-2y)^2-(x+y-2z)(y+z-2x)- (y+z-2x)(z+x-2y)-(z+x-2y)(x+y-2z)] =0 所以（x+y-2z)^3+(y+z-2x)^3+(z+x-2y)^3=3（x+y-2z)(y+z-2x)(z+x-2y) 回答人：潇湘诗社 ☆国士无双卍 有疑问欢迎追问,