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Let ; then when . So is decreasing for ; as , , i.e. .
Looks to me that y = x^(1/x) has a single maximum at x = e.
From here it is an ugly calculus problem.
You mean e^e is always bigger than pi^pi?but why?
This one has been around for a long time. The standard answer starts with raising both sides to the power of
after that it is a maxima-minima problem.
What is the solution of this problem?and how is the problem solved-