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integer polynomial with root \sqrt2+\sqrt3 has also \sqrt2 - \sqrt3

Source: VI Soros Olympiad 1990-00 R3 11.6 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics

May 28, 2024
algebrapolynomialInteger Polynomial

Problem Statement

Let P(x)P(x) be a polynomial with integer coefficients. It is known that the number 2+3\sqrt2+\sqrt3 is its root. Prove that the number 2−3\sqrt2-\sqrt3 is also its root.
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