Difference between revisions of "2023 SSMO Accuracy Round Problems/Problem 6"
(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== | ==Problem== | ||
| − | Let the roots of <math>P(x) = x^3 - 2023x^2 + 2023^{2023}</math> be <math> | + | Let the roots of <math>P(x) = x^3 - 2023x^2 + 2023^{2023}</math> be <math>\alpha, \beta, \gamma.</math>. |
Find | Find | ||
| − | <cmath>\frac{ | + | <cmath>\frac{\alpha^2 + \beta^2}{\alpha + \beta} + \frac{\beta^2 + \gamma^2}{\beta+\gamma} + \frac{\gamma^2 + \alpha^2}{\gamma + \alpha}</cmath> |
==Solution== | ==Solution== | ||
Revision as of 13:46, 23 December 2023
Problem
Let the roots of 
be 
.
Find
![\[\frac{\alpha^2 + \beta^2}{\alpha + \beta} + \frac{\beta^2 + \gamma^2}{\beta+\gamma} + \frac{\gamma^2 + \alpha^2}{\gamma + \alpha}\]](http://latex.artofproblemsolving.com/c/b/9/cb9a83120ec6b7523b4b0afee9639ff451323c1a.png)
