# I find geometry a bit interesting

Geometry Level pending

Let the equation $$x^{3} + y^{3} + 3xy = 1$$ represents the co-ordinate of one vertex $$A$$ and the equation of a side $$BC$$ of the triangle $$ABC$$.

If locus of centroid of triangle $$ABC$$ is $$ax^{3} + by^{3}+ cx^{2} + dx + ey + f = 0$$. Then find the value of $$a + b + c + d + e$$.

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