Difference between revisions of "2023 SSMO Accuracy Round Problems/Problem 6"
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==Solution== | ==Solution== | ||
| + | By Vieta's Relation we get, <math>\sum_{cyc}{}\alpha=2023,</math> <math>\sum_{cyc}{}\alpha\beta=0</math> and <math>\prod_{cyc}{}\alpha=-2023^{2023}</math> Therefore we have to find the value of <cmath>\sum_{cyc}{}\left(\frac{\alpha^2+\beta^2}{\alpha+\beta}\right)\implies </cmath> | ||
Revision as of 13:50, 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)
Solution
By Vieta's Relation we get, 
and 
Therefore we have to find the value of ![\[\sum_{cyc}{}\left(\frac{\alpha^2+\beta^2}{\alpha+\beta}\right)\implies\]](http://latex.artofproblemsolving.com/e/2/f/e2f10f4938bc5be5123bb1baae5df895feae3fa1.png)
