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2025 AIME II Problems/Problem 15

Revision as of 21:58, 13 February 2025 by Dondee123 (talk | contribs) (Created page with "== Problem == Let <cmath>f(x)=\frac{(x-18)(x-72)(x-98)(x-k)}{x}.</cmath>There exist exactly three positive real values of <math>k</math> such that <math>f</math> has a minimum...")
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Problem

Let \[f(x)=\frac{(x-18)(x-72)(x-98)(x-k)}{x}.\]There exist exactly three positive real values of $k$ such that $f$ has a minimum at exactly two real values of $x$. Find the sum of these three values of $k$.

Solution

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