Problem 9
Let=
x and y
be positive real numbers satisfying the inequality ![](3D"2007prob9_files/image002.gif")
. Prove that ![](3D"2007prob9_files/image004.gif")
.
[Problem submitted b=
y Iris
Magee, LACC Professor of Mathematics.]
Solution for Prob=
lem 9:
Now=
implies that ![](3D"2007prob9_files/image007.gif")
.
Thus ![](3D"2007prob9_files/image009.gif")
, so ![](3D"2007prob9_files/image011.gif")
and
![](3D"2007prob9_files/image013.gif")
In
particular ![](3D"2007prob9_files/image015.gif")
and ![](3D"2007prob9_files/image017.gif")
Fin=
ally ![](3D"2007prob9_files/image019.gif")
so =
![](3D"2007prob9_files/image021.gif")
=
and=
![](3D"2007prob9_files/image023.gif")
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////////////////////////////////////////////////////////////////////////////
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