VMO 1994 Problem 1

Find all real solutions to: $x^3$ + 3x - 3 + ln( $x^2$ - x + 1) = y $y^3$ + 3y - 3 + ln( $y^2$ - y + 1) = z $z^3$ + 3z - 3 + ln( $z^2$ - z + 1) = x.

Community text Kalva (prase.cz mirror). 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.