a,b,c≠0,a^3+b^3+c^3=3abc,求a+b+c
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a,b,c≠0,a^3+b^3+c^3=3abc,求a+b+c
a,b,c≠0,a^3+b^3+c^3=3abc,求a+b+c
a,b,c≠0,a^3+b^3+c^3=3abc,求a+b+c
a³+b³+c³-3abc
=(a+b)³+c³-3ab(a+b)-3abc
=(a+b+c)³-3(a+b)c(a+b+c)-3ab(a+b+c)
=(a+b+c)[(a+b+c)²-3c(a+b)-3ab]
=(a+b+c)(a²+b²+c²-ab-bc-ca)
=0.
∴a+b+c=0.