olymmath

JBMO-SL 2009 A3

Find all values of the real parameter aa, for which the system

{(∣x∣+∣y∣−2)2=1y=ax+5\left\{\begin{array}{c} (|x|+|y|-2)^{2}=1 \\ y=a x+5 \end{array}\right.

has exactly three solutions.

Dataset text NuminaMath olympiads. Quoted with source.

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a=5 \text{ or } a=-5

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