1969 Canadian MO Problems/Problem 2
Contents
[hide]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
Solution 3
Plugging in for both of the expressions, we get that
and
. Since
,
is greater
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1969 Canadian MO (Problems) | ||
Preceded by Problem 1 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • | Followed by Problem 3 |