MathDB

2

Part of 1964 Vietnam National Olympiad

Problems(1)

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

Source: Vietnamese MO (VMO) 1964

8/22/2018
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.
algebraQuadraticparametric equation