Question 992727
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It is because the arithmetic mean and geometric mean are really different means.


See the lesson &nbsp;<A HREF=http://www.algebra.com/algebra/homework/Average/Difference-between-Amean-and-Gmean.lesson>Difference between Arithmetic mean and Geometric mean</A>&nbsp; in this site, &nbsp;may be it will help.


See also two more lessons in this site 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Inequalities/Arithmetic-mean-and-geometric-mean-inequality.lesson>Arithmetic mean and geometric mean inequality</A> and

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Inequalities/Arithmetic-mean-and-geometric-mean-inequality-Geometric-interpretations.lesson>Arithmetic mean and geometric mean inequality - Geometric interpretations</A>

if you really want to know more about these means.