Prove that for all positive x, y, and z,
(x+y)^z+(y+z)^x+(z+x)^y > 2.
(In reply to
re(3): Can get close to 2 by pcbouhid)
Sorry, but I have not posted any solution yet. I showed that you
can get as close as you like to 2, but have not shown that you could
not get less than 2. However, see my "Conjecture" post.
I also offer the following extra conjecture: when x,y,z are all
positive, calculus will show that no point is a relative
extremum, and the same is true if z, say, is zero and x and y are
positive. This only leaves the axes. I have now given what is almost a
spoiler, I think, but the derivatives need to be calculated and
examined.
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Posted by Richard
on 2005-03-17 19:05:55 |
re(4): Can get close to 2
