Two Roots Past Two

★ 7/10functions Substitution Absolute Value algebra

Problem

Let $f(x) = x|x - 4|$ for $x \in \mathbb{R}$ . Suppose a positive real $k$ makes the equation $f(x) = k$ have two solutions $a < b$ in $(2, +\infty)$ . Find the range of possible values of

ab - 2(a + b).

Answer

Solution

Difficulty	7/10
Topics	functions, Substitution, Absolute Value, algebra

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