# A strange equation IV

Algebra Level 5

The five real roots of the polynomial $$P(x)=x^{5}-15x^{4}+70x^{3}-90x^{2}-55x-32\sqrt{2}+57$$ can be expressed as: $$x_{1}=a-b\cos(d)$$ , $$x_{2}=a-c\sqrt{c}$$ , $$x_{3}=a+b\cos(e)$$ , $$x_{4}=a+b\cos(f)$$ , $$x_{5}=a+b\cos(g)$$, $$x_{1}<x_{2}<x_{3}<x_{4}<x_{5}$$ and $$0°<d,e,f,g<90°$$. All the variables are positive integer numbers and the angles are in degrees. Find $$d+e+f+g-a-b-c$$.

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