Problem No 52

Algebra Level 3

Suppose $$a,b$$ and $$c$$ are the roots of $$x^3 - 4x + 1 = 0$$, find the value of $\dfrac{a^2 bc}{a^3+1} + \dfrac{ab^2 c}{b^3+1} + \dfrac{abc^2}{c^3+1}.$

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