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.
by
Alan Enrique Ontiveros S…
