RMO 2019 Problem 1

Suppose $x$ is a non zero real number such that both $x^5$ and $20x+\frac{19}{x}$ are rational numbers. Prove that $x$ is a rational number.

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.