SE-SKOLORNAS 1968 Problem 1

Find the maximum and minimum values of $x^2 + 2y^2 + 3z^2$ for real $x, y, z$ satisfying $x^2 + y^2 + z^2 = 1$ .

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.