Don't Hug Me I'm Scared

Geometry Level 5

\[ x^9 - 3x^7 - 30x^6 + 3x^5 - 30x^4 + 299x^3 - 30x^2 + 600x -990 \]

Consider a triangle whose sides are \( a,b,c \), the real roots of the equation above. For nomenclature, consider that opposed to the side \( x \) lies the angle \( X \).

Evaluate \[ \dfrac{\cos\left( \dfrac{A-C}{2} \right) }{\cos \left(\dfrac{A+C}{2} \right)} \]


This problem is not original.
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