CMOQR 2019 Problem 3

Let $f(x) = x^3 + 3x^2 - 1$ have roots $a,b,c$ . (a) Find the value of $a^3 + b^3 + c^3$ (b) Find all possible values of $a^2b + b^2c + c^2a$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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