Problem #PRU-115512

Problems Algebra and arithmetic Algebraic inequalities and systems of inequalities Algebraic inequalities (other)

Problem

Prove that if the numbers $x, y, z$ satisfy the following system of equations for some values of $p$ and $q$ : $\begin{aligned} y & = x^{2} + p x + q, \\ z & = y^{2} + p y + q, \\ x & = z^{2} + p z + q, \end{aligned}$ then the inequality $x^{2} y + y^{2} z + z^{2} x \geq x^{2} z + y^{2} x + z^{2} y$ is satisfied.

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