ILL 1992 Problem 36

Find all rational solutions of $a^2 + c^2 + 17(b^2 + d^2) = 21,$ $ab + cd = 2.$

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.