Again the same

Geometry Level 4

$x^3-24x^2+180x-420=0$

A $$\triangle ABC$$ has side lengths $$a$$, $$b$$ and $$c$$, which are also the roots of the equation above. Find $$a(\cos C+\cos B)+b(\cos C+\cos A)+c(\cos A+\cos B)$$. Give your answer to two decimal places.

Inspiration.

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