试证明(x+y-2z)+(y+z-2x)+(z+x-2y)=3(x+y-2z)(y+z-2x)(z+x-2y)
人气:444 ℃ 时间:2020-02-04 07:47:55
解答
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,
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