Difference between revisions of "2022 SSMO Team Round Problems/Problem 10"
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==Problem== | ==Problem== | ||
| − | If <math> | + | If <math>\alpha, \beta, \gamma</math> are the roots of the polynomial <math>x^3-2x^2-4</math>, find <cmath>(\alpha^3+\beta\gamma)(\beta^3+\gamma\alpha)(\gamma^3+\alpha\beta).</cmath> |
==Solution== | ==Solution== | ||
Revision as of 10:15, 25 December 2023
Problem
If 
are the roots of the polynomial 
, find ![\[(\alpha^3+\beta\gamma)(\beta^3+\gamma\alpha)(\gamma^3+\alpha\beta).\]](http://latex.artofproblemsolving.com/a/4/6/a463ccc3de2f3710c58da87d8e3465af873f82ad.png)
