Question 10
Determine all real polynomials $P(x)$ such that
$$
P^2(x) + P^2(y) + P^2(x + y) = 2P(x^2 + xy + y^2)
$$
for every $x, y \in \mathbb{R}$.
$$
P^2(x) + P^2(y) + P^2(x + y) = 2P(x^2 + xy + y^2)
$$
for every $x, y \in \mathbb{R}$.
MathNet 2025 — Part 01 (100 complete bilingual questions) Question 10
Math Olympiad Vault · MathNet 2025 — Part 01 (100 complete bilingual questions)