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Serbia JBMO TST
2018 Serbia JBMO TST
2
Inequality
Inequality
Source: Serbian JBMO TST 2018, problem 2
May 21, 2018
inequalities
algebra
Serbian competition
Problem Statement
Show that for
a
,
b
,
c
>
0
a,b,c > 0
a
,
b
,
c
>
0
the following inequality holds:
a
b
a
+
b
+
2
c
+
b
c
b
+
c
+
2
a
+
c
a
c
+
a
+
2
b
≤
3
4
\frac{\sqrt{ab}}{a+b+2c}+\frac{\sqrt{bc}}{b+c+2a}+\frac{\sqrt{ca}}{c+a+2b} \le \frac {3}{4}
a
+
b
+
2
c
ab
+
b
+
c
+
2
a
b
c
+
c
+
a
+
2
b
c
a
≤
4
3
.
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