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x is rational if x^2+x, x^3+2x are rationals 2002 Romania District VIII p2

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August 15, 2024
algebrarationalirrational number

Problem Statement

a) Let xx be a real number such that x2+xx^2+x and x3+2xx^3+2x are rational numbers. Show that xx is a rational number.
b) Show that there exist irrational numbers xx such that x2+xx^2+xand x3āˆ’2xx^3-2x are rational.
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