Simon’s proof that Phi is not transcendental

Simon has come up with a proof that Phi (the Golden Ratio) is an algebraic number (not transcendental). He proves it by showing that Phi can be the solution to a polynomial equation (which would be impossible if it was a transcendental number). Indeed, if you simplify Simon’s polynomial further, you can get x squared minus x equals one, which describes one of Phi’s remarkable qualities: the square of Phi (an infinite irrational fraction) equals exactly Phi plus 1. In fact, Simon has talked about this in his previous video (expressing Fibonacci sequence using Lucas Numbers):