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system (x^{2}+y^{2})^{2}-xy(x+y)^{2}=19 and | x - y | = 1

Source: Greece JBMO TST 2014 p1

April 29, 2019
algebrasystem of equationsSolve system

Problem Statement

Find all the pairs of real numbers (x,y)(x,y) that are solutions of the system: (x2+y2)2−xy(x+y)2=19(x^{2}+y^{2})^{2}-xy(x+y)^{2}=19 ∣x−y∣=1| x - y | = 1
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