If a+b+c=0 then prove that a³+b³+c³=3abc
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We know,
a 3 +b 3 +c 3 −3abc=(a+b+c)(a 2 +b 2 −ab−bc−ca)
Putting a+b+c=0 on RHS, we get,
a 3 +b 3 +c 3 −3abc=0
⟹a 3+b 3 +c 3 =3abc, Hence proved.
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