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P(xy)^2 \leq P(x^2)P(y^2)

Source: ARMO 1997, 9.1

April 20, 2013
quadraticsalgebrapolynomialinequalitiesalgebra proposed

Problem Statement

Let P(x)P(x) be a quadratic polynomial with nonnegative coeficients. Show that for any real numbers xx and yy, we have the inequality P(xy)2⩽P(x2)P(y2)P(xy)^2 \leqslant P(x^2)P(y^2). E. Malinnikova
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