[/quote]
,
be real numbers such that 
Prove that
Where 
Where 
are are the lengths of the sides of a 
g
then![$$(n-2)\left[\sum_{i=1}^{n}{\frac{a_i^2}{(1-a_i)^2}}-\frac n{(n-1)^2}\right]\geq(2n-1)\left(\sum_{i=1}^{n}{\frac{a_i}{1-a_i}}-\frac n{n-1}\right)^2.$$](http://latex.artofproblemsolving.com/9/3/e/93e5529518807b92cd9e0382f5fb07a293128b04.png)
be an acute triangle. Tangents on the circumscribed circle of triangle 
and 
intersect at point 
.
and 
be a foot of the altitudes from 
and 
and let 
be the midpoint of 
.
.
cuts 
in half.
and 
.
be an irrational number. Show that for every integer 
,
such that 
.
be positive integers with 
,
of the set of 
”
”
(i dont remember exactly if it was 8032038 or some other number, so correct me on this)
(i posted this at 12:29) lol
?
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This post has been edited 13 times. Last edited by AkshajK, Nov 3, 2012, 11:05 AM
