1969 Canadian MO Problems/Problem 2
Revision as of 21:45, 19 December 2022 by Hastapasta (talk | contribs)
Problem
Determine which of the two numbers ,
is greater for any
.
Solution 1
Multiplying and dividing by its conjugate,
Similarly, . We know that
for all positive
, so
.
Solution 2
Considering the derivative of .
We have . Putting under a common denominator, we can see that the top will be negative.
Thus is greater.
~hastapasta
1969 Canadian MO (Problems) | ||
Preceded by Problem 1 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • | Followed by Problem 3 |