已知x^2-y^2-z^2=0,A是关于x,y,z的一次多项式,且x^3-y^3-z^3=(x-y)(x-z)A,则A的表达式是()
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![已知x^2-y^2-z^2=0,A是关于x,y,z的一次多项式,且x^3-y^3-z^3=(x-y)(x-z)A,则A的表达式是()](/uploads/image/z/5430873-57-3.jpg?t=%E5%B7%B2%E7%9F%A5x%5E2-y%5E2-z%5E2%3D0%2CA%E6%98%AF%E5%85%B3%E4%BA%8Ex%2Cy%2Cz%E7%9A%84%E4%B8%80%E6%AC%A1%E5%A4%9A%E9%A1%B9%E5%BC%8F%2C%E4%B8%94x%5E3-y%5E3-z%5E3%3D%28x-y%29%28x-z%29A%2C%E5%88%99A%E7%9A%84%E8%A1%A8%E8%BE%BE%E5%BC%8F%E6%98%AF%EF%BC%88%EF%BC%89)
已知x^2-y^2-z^2=0,A是关于x,y,z的一次多项式,且x^3-y^3-z^3=(x-y)(x-z)A,则A的表达式是()
已知x^2-y^2-z^2=0,A是关于x,y,z的一次多项式,且x^3-y^3-z^3=(x-y)(x-z)A,则A的表达式是()
已知x^2-y^2-z^2=0,A是关于x,y,z的一次多项式,且x^3-y^3-z^3=(x-y)(x-z)A,则A的表达式是()
x^2-y^2-z^2=0
(x^2-y^2-z^2)(x+y+z)=0
x^3-y^3-z^3+x^2*y+x^2*z-y^2*x-y^2*z-z^2*x-z^2*y=0
x^3-y^3-z^3=-x^2*y-x^2*z+y^2*x+y^2*z+z^2*x+z^2*y
-x^2*y-x^2*z+y^2*x+y^2*z+z^2*x+z^2*y=(x-y)(x-z)A
可解
因为x^2-y^2-z^2=0
所以z^3=z(x^2-y^2) y^2=x^2-z^2
因为X^3-Y^3-Z^3=(X-Y)(X-Z)A
所以x^3-y^3-z(x^2-y^2)=(x-y)(x-z)A
则(x-y)(x^2+xy+y^2)-(x-y)(zx+zy)=(X-Y)(x-Z)A
所以(x-y)[x^2+(y-z)x+y^2-yz]=...
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因为x^2-y^2-z^2=0
所以z^3=z(x^2-y^2) y^2=x^2-z^2
因为X^3-Y^3-Z^3=(X-Y)(X-Z)A
所以x^3-y^3-z(x^2-y^2)=(x-y)(x-z)A
则(x-y)(x^2+xy+y^2)-(x-y)(zx+zy)=(X-Y)(x-Z)A
所以(x-y)[x^2+(y-z)x+y^2-yz]=(X-Y)(x-Z)A
(x-y)[x^2+(y-z)x+x^2-z^2-yz]=(X-Y)(x-Z)A
(x-y)(x-z)(2x+y+z)=(x-y)(x-z)A
所以A=2x+y+z
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