olymmath

JBMO-SL 2008 A3

  • Answer

Let the real parameter pp be such that the system

{p(x2−y2)=(p2−1)xy∣x−1∣+∣y∣=1\left\{\begin{array}{l} p\left(x^{2}-y^{2}\right)=\left(p^{2}-1\right) x y \\ |x-1|+|y|=1 \end{array}\right.

has at least three different real solutions. Find pp and solve the system for that pp.

Dataset text NuminaMath olympiads. Quoted with source.

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p=1 \text{ or } p=-1, \text{ and } 0 \leq x \leq 1, \text{ and } y = \pm x

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