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2023 WSMO Accuracy Round Problems/Problem 3

Revision as of 15:35, 2 May 2025 by Pinkpig (talk | contribs) (Created page with "==Problem== <math>f(x)=x^3-8x^2+10x-4</math> has complex roots <math>a,b,c</math>. Denote <math>P(n) = a^n+b^n+c^n.</math> Find <math>P(-1)P(0)P(1).</math> ==Solution==")
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Problem

$f(x)=x^3-8x^2+10x-4$ has complex roots $a,b,c$. Denote $P(n) = a^n+b^n+c^n.$ Find $P(-1)P(0)P(1).$

Solution

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