2016 AIME II Problems/Problem 15
Contents
[hide]Problem
For let and . Let be positive real numbers such that and . The maximum possible value of , where and are relatively prime positive integers. Find .
Solution
Note that Substituting this into the second equation and collecting terms, we find Conveniently, so we find This is the equality case of the Cauchy-Schwarz Inequality, so for some constant . Summing these equations and using the facts that and , we find and thus . Hence the desired answer is .
Video Solution
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See Also
2016 AIME II (Problems • Answer Key • Resources) | ||
Preceded by Problem 14 |
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