Given a polynomial $P(x)$ with positive real coefficients. Prove that $P(1)P(xy) \ge P(x)P(y)$ for all $x\ge1, y \ge 1$. (K. Gorodnin)
Source: 2012 Belarus TST 2.3
Tags: algebra, inequalities, polynomial
Given a polynomial $P(x)$ with positive real coefficients. Prove that $P(1)P(xy) \ge P(x)P(y)$ for all $x\ge1, y \ge 1$. (K. Gorodnin)