Tricky system

Algebra Level 5

Let aa, bb and cc be positive real numbers that satisfy the following equations: a2+b2+3ab=727a^2+b^2+\sqrt{3}ab=727 a2+c2+3ac=829a^2+c^2+\sqrt{3}ac=829 b2+c2bc=39b^2+c^2-bc=39 If a+b+c=d+f3a+b+c=d+f \sqrt{3}, find dfdf.

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