Lemma › Problems › Prove that if a+b+c = 0 then (a^2+b^2+c^2)/(2) · (a^5+b^5+c^5)/(5) =…

Classic olympiad problem · Algebra

Prove that if a+b+c = 0 then (a^2+b^2+c^2)/(2) · (a^5+b^5+c^5)/(5) =…

Prove that if

a+b+c = 0

then

\dfrac{a^2+b^2+c^2}{2} \cdot \dfrac{a^5+b^5+c^5}{5} = \dfrac{a^7+b^7+c^7}{7}

Topic: Algebra Difficulty: 5/6 Expected time: ~45 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.

Train it on Lemma

This problem sits in the Olympiad Set — 81 real competition problems with progressive hints, full walkthroughs and marking rubrics. 78 lessons, 624 curated problems and unlimited generated practice at six difficulties. Free to start — no card, no trial clock.

Find your level

Prove that if a+b+c = 0 then (a^2+b^2+c^2)/(2) · (a^5+b^5+c^5)/(5) =…

Train it on Lemma

More Algebra problems