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find number of roots x + | x^2 - 1 | = k, k real

Source: Vietnamese MO (VMO) 1964

August 22, 2018
algebraQuadraticparametric equation

Problem Statement

Draw the graph of the functions y=∣x2−1∣y = | x^2 - 1 | and y=x+∣x2−1∣y = x + | x^2 -1 |. Find the number of roots of the equation x+∣x2−1∣=kx + | x^2 - 1 | = k, where kk is a real constant.
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