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non linear system with parameter

Source: Vietnam MO 1978 P2

July 29, 2018
algebrasystem of equationsparameterization

Problem Statement

Find all values of the parameter mm such that the equations x2=2∣x∣+∣x∣−y−m=1−y2x^2 = 2^{|x|} + |x| - y - m = 1 - y^2 have only one root.
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