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Inequality with polynomial

Source: 2023 Turkey Egmo Tst P4

March 23, 2023

inequalitiesalgebrapolynomial

Problem Statement

Let

n

be a positive integer and

P,Q

be polynomials with real coefficients with

P(x)=x^nQ(\frac{1}{x})

and

P(x) \geq Q(x)

for all real numbers

x

. Prove that

P(x)=Q(x)

for all real number

x

.

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