$P(x),Q(x)$ are two polynomials such that $P(x) = Q(x)$ has no real solution,and $P(Q(x)) \equiv Q(P(x))$ $\forall x \in \mathbb{R}$.
Prove that $P(P(x)) = Q(Q(x))$ has no real solution.
Polynomials without real solutions
"Questions we can't answer are far better than answers we can't question"
Re: Polynomials without real solutions
My solution:
Comment:
The first principle is that you must not fool yourself and you are the easiest person to fool.