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x^3+y^3+z^3-3xyz用轮换对称式怎么解?

2008-07-05 16:41:29l***
x^3+y^3+z^3-3xyz用轮换对称式怎么解?：　x³+y³+z³-3xyz = [(x+y)³-3xy(x+y?

最佳回答

  • 　x³+y³+z³-3xyz = [(x+y)³-3xy(x+y)] + z³-3xyz = [(x+y)³+z³] - 3xy(x+y+z) = [(x+y+z)³-3(x+y)z(x+y+z)] - 3xy(x+y+z) = (x+y+z)³-3(xy+yz+zx)(x+y+z) = (x+y+z)[(x+y+z)²-3(xy+yz+zx)] = (x+y+z)(x²+y²+z²-xy-yz-zx)
    2008-07-05 17:01:18
  • x^3+y^3+z^3-3xyz 这个是全对称，没有轮换对称式。
    2008-07-05 16:58:04
    • 很赞哦！ (82)

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