Lemma › Problems › Let a,b,c be reals with a+b+c = 0. Prove that a^3+b^3+c^3 = 3abc.

Classic olympiad problem · Algebra

Let a,b,c be reals with a+b+c = 0. Prove that a^3+b^3+c^3 = 3abc.

Let

a,b,c

be reals with

a+b+c = 0

. Prove that

a^3+b^3+c^3 = 3abc

Topic: Algebra Difficulty: 4/6 Expected time: ~35 min Progressive hints on Lemma: 3

This is a proof problem — the answer is an argument, not a number. The solution is deliberately not posted here: reading a solution you didn't fight for teaches almost nothing. On Lemma you attempt it cold, take one of the 3 progressive hints only when genuinely stuck, then compare your proof against a full walkthrough and mark yourself with the same rubric a competition coordinator would use.

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Let a,b,c be reals with a+b+c = 0. Prove that a^3+b^3+c^3 = 3abc.

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