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Question

If a+b+c=0 then prove that a3+b3+c3=3abc.

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Solution

Given a+b+c=0
or, a+b=c.......(1).
Now cubing both sides we get,
(a+b)3=c3
or, a3+b3+3ab(a+b)=c3
or, a3+b33abc=c3 [ Using (1)]
or, a3+b3+c3=3abc.

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