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2023 SSMO Accuracy Round Problems/Problem 6

Revision as of 21:21, 15 December 2023 by Pinkpig (talk | contribs) (Created page with "==Problem== Let the roots of <math>P(x) = x^3 - 2023x^2 + 2023^{2023}</math> be <math>p, q, r</math>. Find <cmath>\frac{p^2 + q^2}{p + q} + \frac{q^2 + r^2}{q + r} + \frac{r^2...")
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Problem

Let the roots of $P(x) = x^3 - 2023x^2 + 2023^{2023}$ be $p, q, r$. Find \[\frac{p^2 + q^2}{p + q} + \frac{q^2 + r^2}{q + r} + \frac{r^2 + p^2}{r + p}\]

Solution

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