Let n be an integer greater than or equal to 2 . Peove that if the real numbers $a_1,a_2,...,a_n$ satisfy \[ a_1^2+a_2^2+...+a_n^2=n\] , then
\[\sum_{1\leq i < j \leq n} \frac{1}{n-a_ia_j} \leq \frac{n}{2}\]
must hold .
APMO 2012/05
Discussion on Asian Pacific Mathematical Olympiad (APMO)
- Nadim Ul Abrar
- Posts:244
- Joined:Sat May 07, 2011 12:36 pm
- Location:B.A.R.D , kotbari , Comilla
Unread post by Nadim Ul Abrar » Sat May 19, 2012 12:48 am
$\frac{1}{0}$
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