small ship sails on a polynomial determined coordinate
Source: Tuymaada 2023 Senior P5
July 8, 2023
analytic geometrypolynomialalgebraTuymaada
Problem Statement
A small ship sails on an infinite coordinate sea. At the moment the ship is at the point with coordinates , where and are two polynomials of third degree. Yesterday at the ship was at the same point as at , and at , it was at the same point as at . Prove that the ship sails along a straight line.