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2022 SSMO Team Round Problems/Problem 7

Revision as of 12:06, 14 December 2023 by Pinkpig (talk | contribs) (Created page with "==Problem== Let <math>\cos(2A)</math>, <math>\cos(2B)</math>, and <math>\cos(2C)</math> be the not necessarily distinct roots of a monic cubic <math>f</math>. Given that <math...")
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Problem

Let $\cos(2A)$, $\cos(2B)$, and $\cos(2C)$ be the not necessarily distinct roots of a monic cubic $f$. Given that $f(1)= \frac{17}{30}$, the value of $\sin(A)\sin(B)\sin(C)$ can be expressed as $\frac{\sqrt{m}}{n},$ with $m$ squarefree. Find $m+n$.

Solution

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