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2006 Bulgaria Team Selection Test
2
Tough ineq
Tough ineq
Source: Bulgarian TST1/2006 Problem 5
May 31, 2006
inequalities
inequalities unsolved
algebra
Problem Statement
Prove that if
a
,
b
,
c
>
0
,
a,b,c>0,
a
,
b
,
c
>
0
,
then
a
b
3
a
+
4
b
+
5
c
+
b
c
3
b
+
4
c
+
5
a
+
c
a
3
c
+
4
a
+
5
b
≤
a
+
b
+
c
12
.
\frac{ab}{3a+4b+5c}+\frac{bc}{3b+4c+5a}+\frac{ca}{3c+4a+5b}\le \frac{a+b+c}{12}.
3
a
+
4
b
+
5
c
ab
+
3
b
+
4
c
+
5
a
b
c
+
3
c
+
4
a
+
5
b
c
a
≤
12
a
+
b
+
c
.
Nikolai Nikolov
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