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Geometry Level 5

A regular pentagon "P" has a side length of 2. A new regular hexagon "Q" is made with the side equal to the diagonal of the pentagon "P". The ratio of the area of the hexagon "Q" by the perimeter of pentagon "P" can be expressed as \(\frac { A }{ B } (3\sqrt { 3 } +\sqrt { C } )\).

A third degree polynomial equation that gives us the A,B and C as roots can be written by: \({ x }^{ 3 }+a{ x }^{ 2 }+bx+c\).

Find a+b+c

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