# Tricky system

Algebra Level 5

Let $$a$$, $$b$$ and $$c$$ be positive real numbers that satisfy the following equations: $a^2+b^2+\sqrt{3}ab=727$ $a^2+c^2+\sqrt{3}ac=829$ $b^2+c^2-bc=39$ If $$a+b+c=d+f \sqrt{3}$$, find $$df$$.

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