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计算(x-y)^2/(z-x)(z-y)+(y-z)^2/(x-y)(x-z)+(z-x)^2/(y-x)(y-z)
题目详情
计算(x-y)^2/(z-x)(z-y)+(y-z)^2/(x-y)(x-z)+(z-x)^2/(y-x)(y-z)
▼优质解答
答案和解析
(x-y)^2/(z-x)(z-y)+(y-z)^2/(x-y)(x-z)+(z-x)^2/(y-x)(y-z)
=[-(x-y)^3-(y-z)^3-(z-x)^3]/[(x-y)(y-z)(z-x)]
=[-x^3+3x^2y-3xy^2+y^3-y^3+3y^2z-3yz^2+z^3-z^3+3z^2x-3zx^2+x^3]/[(x-y)(y-z)(z-x)]
=[3x^2y-3xy^2+3y^2z-3yz^2+3z^2x-3zx^2]/[(x-y)(y-z)(z-x)]
=3[x^2y-xy^2+y^2z-yz^2+z^2x-zx^2]/[(x-y)(y-z)(z-x)]
=3[xy(x-y)+yz(y-z)+zx(z-x)]/[(x-y)(y-z)(z-x)]
只能这样了,去掉立方项
=[-(x-y)^3-(y-z)^3-(z-x)^3]/[(x-y)(y-z)(z-x)]
=[-x^3+3x^2y-3xy^2+y^3-y^3+3y^2z-3yz^2+z^3-z^3+3z^2x-3zx^2+x^3]/[(x-y)(y-z)(z-x)]
=[3x^2y-3xy^2+3y^2z-3yz^2+3z^2x-3zx^2]/[(x-y)(y-z)(z-x)]
=3[x^2y-xy^2+y^2z-yz^2+z^2x-zx^2]/[(x-y)(y-z)(z-x)]
=3[xy(x-y)+yz(y-z)+zx(z-x)]/[(x-y)(y-z)(z-x)]
只能这样了,去掉立方项
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