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National and Regional Contests
Romania Contests
Romania National Olympiad
2021 Romania National Olympiad
3
Romanian NMO 2021 inequality
Romanian NMO 2021 inequality
Source:
April 25, 2021
inequalities
algebra
Problem Statement
If
a
,
b
,
c
>
0
,
a
+
b
+
c
=
1
a,b,c>0,a+b+c=1
a
,
b
,
c
>
0
,
a
+
b
+
c
=
1
,then:
1
a
b
c
+
4
a
2
+
b
2
+
c
2
≥
13
a
b
+
b
c
+
c
a
\frac{1}{abc}+\frac{4}{a^{2}+b^{2}+c^{2}}\geq\frac{13}{ab+bc+ca}
ab
c
1
+
a
2
+
b
2
+
c
2
4
≥
ab
+
b
c
+
c
a
13
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