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2012 District Olympiad
2
Sum less than 3/4.
Sum less than 3/4.
Source: Romanian District Olympiad 2012, Grade IX, Problem 2
October 9, 2018
inequalities
algebra
Problem Statement
If
a
,
b
,
c
>
0
,
a,b,c>0,
a
,
b
,
c
>
0
,
then
∑
cyc
a
2
a
+
b
+
c
≤
3
/
4.
\sum_{\text{cyc}} \frac{a}{2a+b+c}\le 3/4.
∑
cyc
2
a
+
b
+
c
a
≤
3/4.
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