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p(x^2 - y^2) = (p^2- 1)xy , |x - 1|+ |y| = 1

Source: JBMO 2008 Shortlist A3

October 14, 2017
JBMOsystem of equationsalgebra

Problem Statement

Let the real parameter pp be such that the system {p(x2−y2)=(p2−1)xy∣x−1∣+∣y∣=1\begin{cases} p(x^2 - y^2) = (p^2- 1)xy \\ |x - 1|+ |y| = 1 \end{cases} has at least three different real solutions. Find pp and solve the system for that pp.
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