1989 USAMO Problems/Problem 5
Let and be real numbers such that Determine, with proof, which of the two numbers, or , is larger.
The answer is .
We define real functions and as follows: We wish to show that if , then .
We first note that when , , , and , so Similarly, .
We also note that if , then Similarly . It then follows that .
Now, for all , Since and are both strictly increasing functions over the nonnegative reals, it then follows that so , as desired.
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