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Moldova Team Selection Test
2015 Moldova Team Selection Test
2
Inequality with product equal to 1
Inequality with product equal to 1
Source: Moldova TST Problem 6
April 1, 2015
inequalities
Problem Statement
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be positive real numbers such that
a
b
c
=
1
abc=1
ab
c
=
1
. Prove the following inequality: \\
a
3
+
b
3
+
c
3
+
a
b
a
2
+
b
2
+
b
c
b
2
+
c
2
+
c
a
c
2
+
a
2
≥
9
2
a^3+b^3+c^3+\frac{ab}{a^2+b^2}+\frac{bc}{b^2+c^2}+\frac{ca}{c^2+a^2} \geq \frac{9}{2}
a
3
+
b
3
+
c
3
+
a
2
+
b
2
ab
+
b
2
+
c
2
b
c
+
c
2
+
a
2
c
a
≥
2
9
.
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