作业帮x+y+z=0求 x3+y3+z3=?
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x+y+z=0求 x3+y3+z3=?
(x+y+z)^3=0
如果你不知道三项的展开式的话 先把x+y看成一项
（x+y+z）^3
=(x+y)^3+z^3+3(x+y)^2z+3(x+y)z^2
=x^3+y^3+z^3+3x^2y+3xy^2+3(x+y)^2z+3(x+y)z^2
=x^3+y^3+z^3+3xy(x+y)+3(x+y)^2z+3(x+y)z^2
=x^3+y^3+z^3+3(x+y)[xy+(x+y)*z+z^2]
=x^3+y^3+z^3+3(x+y)(xy+xz+yz+z^2)
=x^3+y^3+z^3+3(x+y)(x+z)(y+z)
=0
x^3+y^3+z^3=-3(x+y)(x+z)(y+z)
x+y+z=0
x+y=-z
y+z=-x
x+z=-y
x^3+y^3+z^3=3xyz
按你的意思我只能算出这个结果 不给xyz的乘积 没办法算出具体值
如果你不知道三项的展开式的话 先把x+y看成一项
（x+y+z）^3
=(x+y)^3+z^3+3(x+y)^2z+3(x+y)z^2
=x^3+y^3+z^3+3x^2y+3xy^2+3(x+y)^2z+3(x+y)z^2
=x^3+y^3+z^3+3xy(x+y)+3(x+y)^2z+3(x+y)z^2
=x^3+y^3+z^3+3(x+y)[xy+(x+y)*z+z^2]
=x^3+y^3+z^3+3(x+y)(xy+xz+yz+z^2)
=x^3+y^3+z^3+3(x+y)(x+z)(y+z)
=0
x^3+y^3+z^3=-3(x+y)(x+z)(y+z)
x+y+z=0
x+y=-z
y+z=-x
x+z=-y
x^3+y^3+z^3=3xyz
按你的意思我只能算出这个结果 不给xyz的乘积 没办法算出具体值
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