MathNet 2026 — Part 03 Question 186

Let $x_{1}, x_{2}$ be the roots of the $P(x)=3 x^{2}+3 m x+m^{2}-1$ polynomial, with $m$ being a real number. Prove that $P\left(x_{1}^{3}\right)=P\left(x_{2}^{3}\right)$.