a+b+c=0,证明a^3+b^3+c^3=3abc

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a+b+c=0,证明a^3+b^3+c^3=3abc
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a+b+c=0,证明a^3+b^3+c^3=3abc
a+b+c=0,证明a^3+b^3+c^3=3abc

a+b+c=0,证明a^3+b^3+c^3=3abc
c= -(a+b)
a^3+b^3+c^3
=a^3+b^3-(a+b)^3
=a^3+b^3-(a^3+3a^2b+3ab^2+b^3)
= -(3a^2b+3ab^2)
= -3ab(a+b)
=3abc