自娱自乐的小点
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(a+b+c)^3
=a^3+b^3+c^3+3ab^2+3ba^2+3ac^2+3ca^2+3bc^2+3cb^2+6abc
=a^3+b^3+c^3+(3ab^2+3ba^2+3abc)+(3ac^2+3ca^2+3abc)+(3bc^2+3cb^2+3abc)-3abc
=a^3+b^3+c^3+3ab(a+b+c)+3ac(a+b+c)+3bc(a+b+c)-3abc
由于a+b+c=0
=>
0
=(a+b+c)^3
=a^3+b^3+c^3+3ab(a+b+c)+3ac(a+b+c)+3bc(a+b+c)-3abc
=a^3+b^3+c^3-3abc
=>a^3+b^3+c^3=3abc
1年前
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