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VMO 1964 - Division A Question 2

VMO · VMO 1964 - Division A

Question 2

Draw the graphs of the following functions:
$$u=\sqrt{(x^2-1)^2},\qquad y=x+\sqrt{(x^2-1)^2},\qquad x\in\mathbb R.$$
Discuss the number of solutions of
$$x+\sqrt{(x^2-1)^2}=m$$
as a function of the parameter $m$.