Monthly Archives: September 2025

Prove that there is no polynomial $P(x)$ with integer coefficients such that $$P(\sqrt[3]{5}+\sqrt[3]{25})=2\sqrt[3]{5}+3\sqrt[3]{25}$$🔑 Proof: Assume that there is a polynomial $P(x)$ of degree $n$, with integer coefficients, and without trivial root of $0$, such that$$P(\sqrt[3]{5}+\sqrt[3]{25})=2\sqrt[3]{5}+3\sqrt[3]{25}$$Therefore, $P(x)$ can be expressed as … Continue reading →