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Find real solutions to set of equations

Source: AustriaMO1970 problem 4

June 29, 2011
number theorygreatest common divisoralgebrapolynomialalgorithmalgebra unsolved

Problem Statement

Find all real solutions of the following set of equations: 72x3+4xy2=11y372x^3+4xy^2=11y^3 27x5−45x4y−10x2y3=−14332y527x^5-45x^4y-10x^2y^3=\frac{-143}{32}y^5
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