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

来源：学生作业帮编辑：灵鹊做题网作业帮分类：数学作业时间：2024/04/30 13:35:38

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 ☆國士無雙卍有疑问欢迎追问,

试证明(x+y-2z)+(y+z-2x)+(z+x-2y)=3(x+y-2z)(y+z-2x)(z+x-2y) x,y,z正整数 x>y>z证明 x^2x +y^2y+z^2z>x^(y+z)*y^(x+z)*z^(x+y) (y-x)/(x+z-2y)(x+y-2z)+(z-y)(x-y)/(x+y-2z)(y+z-2x)+(x-z)(y-z 化简(y-x)(z-x)/(x-2y+z)(x+y-2z)+（z-y)(x-y)/(x-2z+y)(y+z-2x)+(x 已知 x,y,z都是正实数,且 x+y+z=xyz 证明 (y+x)/z+(y+z)/x+(z+x)/y≥2(1/x+1 (x-2y+z)(x+y-2z)分之（y-x)(z-x) + (x+y-2z)(y+z-2x)分之(z-y)(x-y) 设x、y、z为整数,证明:x^4*(y-z)+y^4*(z-x)+z^4*(x-y)/(y+z)^2+(z+x)^2+( x/2=y/3=z/5 x+3y-z/x-3y+z 已知(x+y+z)^2=x^2+y^2+z^2,证明x(y+z)+y(z+x)+z(x+y)=0 试证明(x+y-2z)³+(y+z-2x)³+(z+x-2y)³=3(x+y-2z)(y+ 化简(y-x)(z-x)/(x-2y+z)(x+y-2z)+（z-y)(x-y)/(xy-2z)(y+z-2x)+(x- (x+y-z)^2-(x-y+z)^2=?