UA-UMO 2005 Problem 84

For which real numbers $x>1$ is there a triangle with side lengths $x^4+x^3+2x^2+x+1, 2x^3+x^2+2x+1,$ and $x^4-1$ ?

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.