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National and Regional Contests
Serbia Contests
Serbia National Math Olympiad
2022 Serbia National Math Olympiad
P2
Inequality
Inequality
Source: Serbian national olympiad 2022
April 1, 2022
inequalities
Serbian competition
Problem Statement
Let
a
a
a
,
b
b
b
and
c
c
c
be positive real numbers and
a
3
+
b
3
+
c
3
=
3
a^3+b^3+c^3=3
a
3
+
b
3
+
c
3
=
3
. Prove
1
3
−
2
a
+
1
3
−
2
b
+
1
3
−
2
c
≥
3
\frac{1}{3-2a}+\frac{1}{3-2b}+\frac{1}{3-2c}\geq 3
3
−
2
a
1
+
3
−
2
b
1
+
3
−
2
c
1
≥
3
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