# A strange equation II

Algebra Level 5

The three real roots of the polynomial $$P(x)=x^{3}-3x^{2}+1$$ can be expressed as:

$x_{1}=-b\cos(e°)+a , x_{2}=-c\cos(f°)+a, x_{3}=d\cos(g°)+a,$

where $$x_{1}<x_{2}<x_{3}$$, $$0°<e<90°$$, $$0°<f<90°$$, $$0°<g<90°$$, such that $$a$$, $$b$$, $$c$$, $$d$$, $$e$$, $$f$$ and $$g$$ are positive integers; and $$e$$, $$f$$ and $$g$$ are integer degrees. Find $$a+b+c+d+e+f+g$$.

You may also try Part III.

×