已知ax^3=by^3=cz^3,1\x+1\y+1\z,,三次根号(ax^2+by^2+cz^2)与三次根号下a+三次根号下b+三次根号下c的大小关系如何
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![已知ax^3=by^3=cz^3,1\x+1\y+1\z,,三次根号(ax^2+by^2+cz^2)与三次根号下a+三次根号下b+三次根号下c的大小关系如何](/uploads/image/z/5120183-47-3.jpg?t=%E5%B7%B2%E7%9F%A5ax%5E3%3Dby%5E3%3Dcz%5E3%2C1%5Cx%2B1%5Cy%2B1%5Cz%2C%2C%E4%B8%89%E6%AC%A1%E6%A0%B9%E5%8F%B7%28ax%5E2%2Bby%5E2%2Bcz%5E2%29%E4%B8%8E%E4%B8%89%E6%AC%A1%E6%A0%B9%E5%8F%B7%E4%B8%8Ba%2B%E4%B8%89%E6%AC%A1%E6%A0%B9%E5%8F%B7%E4%B8%8Bb%2B%E4%B8%89%E6%AC%A1%E6%A0%B9%E5%8F%B7%E4%B8%8Bc%E7%9A%84%E5%A4%A7%E5%B0%8F%E5%85%B3%E7%B3%BB%E5%A6%82%E4%BD%95)
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已知ax^3=by^3=cz^3,1\x+1\y+1\z,,三次根号(ax^2+by^2+cz^2)与三次根号下a+三次根号下b+三次根号下c的大小关系如何
已知ax^3=by^3=cz^3,1\x+1\y+1\z,
,三次根号(ax^2+by^2+cz^2)与三次根号下a+三次根号下b+三次根号下c的大小关系如何
已知ax^3=by^3=cz^3,1\x+1\y+1\z,,三次根号(ax^2+by^2+cz^2)与三次根号下a+三次根号下b+三次根号下c的大小关系如何
设ax^3=by^3=cz^3=s^3,
∴(ax^2+by^2+cz^2)^1\3
=(s^3/x+s^3/y+s^3/z)^1/3
=[s^3(1/x+1/y+1/z)]^1/3
=s
∵a^1\3+b^1\3+c^1\3
=s/x+s/y+s/z
=s(1/x+1/y+1/z)
=s
∴(ax^2+by^2+cz^2)^1\3=a^1\3+b^1\3+c^1\3.