Difference between revisions of "2025 AIME II Problems/Problem 15"
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== Solution == | == Solution == | ||
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==See also== | ==See also== | ||
{{AIME box|year=2025|num-b=14|after=Last Problem|n=II}} | {{AIME box|year=2025|num-b=14|after=Last Problem|n=II}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 03:09, 14 February 2025
Problem
Let
![\[f(x)=\frac{(x-18)(x-72)(x-98)(x-k)}{x}.\]](http://latex.artofproblemsolving.com/0/d/b/0dbe0a5b2a8136e0b1e02478bc822fe2ba6ada41.png)
There exist exactly three positive real values of 
such that 
has a minimum at exactly two real values of 
. Find the sum of these three values of .
Solution
Alternate solutions are always welcome. If you have a different, elegant solution to this problem, please add it to this page.
See also
| 2025 AIME II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 14 |
Followed by Last Problem | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
