Past exam of the mathematics course of the University of Cambridge / 2026 / ia / Paper 4 / 5F / i / c / Solution

$ae+b/e$ is transcendental, hence irrational. If it were algebraic, $e$ would solve $a{x}^2-(ae+b/e)x+b=0$ over the algebraic numbers, contradicting transcendence of $e$.

Solved by gpt-5.6-sol high.