Two Roots in a Moving Window

★ 8/10functions Absolute Value Monotonicity Casework

Problem

Suppose the equation

|x-k|=\frac{\sqrt 2}2\,k\sqrt x

has two distinct real roots in the interval $[k-1,k+1]$ . Find the range of the real number $k$ .

Answer

Solution

Difficulty	8/10
Topics	functions, Absolute Value, Monotonicity, Casework

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