已知：x+y+z=0,求证：x³+y³+z=3xyz.已知：x+y+z=0,求证：x³+y³+z³=3xyz.

已知：x+y+z=0,求证：x³+y³+z=3xyz.已知：x+y+z=0,求证：x³+y³+z³=3xyz.
已知：x+y+z=0,求证：x³+y³+z=3xyz.
已知：x+y+z=0,求证：x³+y³+z³=3xyz.

已知：x+y+z=0,求证：x³+y³+z=3xyz.已知：x+y+z=0,求证：x³+y³+z³=3xyz.
X^3+Y^3+Z^3=(X+Y)(X^2-XY+Y^2)+Z^3
=-Z((X+Y)^2-3XY)+Z^3
=-Z^3+3XYZ+Z^3
=3XYZ
LZ题目错了吧~Z^3?

x³+y³+z³-3xyz 
=(x³+3x²y+3xy²+y³+z³)-(3xyz+3x²y+3xy²) 
=[(x+y)³+z³]-3xy(x+y+z) 
=(x+y+z)(x²+y²+2xy-xz-yz+z²...

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x³+y³+z³-3xyz 
=(x³+3x²y+3xy²+y³+z³)-(3xyz+3x²y+3xy²) 
=[(x+y)³+z³]-3xy(x+y+z) 
=(x+y+z)(x²+y²+2xy-xz-yz+z²)-3xy(x+y+z) 
=(x+y+z)(x²+y²+z²+2xy-3xy-xz-yz) 
=(x+y+z)(x²+y²+z²-xy-yz-xz)
=0
所以x³+y³+z³=3xyz

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已知：x+y+z=0,求证：x³+y³+z=3xyz
不可能证明的，这个明显错误。X=1,Y=1,Z=-2,代入等式就知道。