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1-ab=rational^2 if a^3b+ab^3+2a^2b2+2a + 2b + 1 = 0

Source: All-Russian MO 2009 Regional 9.2

August 27, 2024
algebraPerfect Square

Problem Statement

Rational numbers aa and bb satisfy the equality a3b+ab3+2a2b2+2a+2b+1=0.a^3b+ab^3+2a^2b^2+2a + 2b + 1 = 0. Prove that the number 1āˆ’ab1-ab is the square of the rational numbers.
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