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(|x| + |y| - 2)^2 = 1 , y = ax + 5

Source: JBMO 2009 Shortlist A3

October 14, 2017
JBMOalgebrasystem of equations

Problem Statement

Find all values of the real parameter aa, for which the system (∣x∣+∣y∣−2)2=1(|x| + |y| - 2)^2 = 1 y=ax+5y = ax + 5 has exactly three solutions
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