A Zero Through a Substitution

★ 7/10functions Substitution Cauchy-Schwarz inequality

Problem

Let $f(u) = u^2 + au + b - 2$ , where $u = x + \dfrac{1}{x}$ for real $x \neq 0$ . If the composite function of $x$ has a zero, find the minimum value of $a^2 + b^2$ .

Answer

Solution

Difficulty	7/10
Topics	functions, Substitution, Cauchy-Schwarz, inequality

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