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2016 239 Open Mathematical Olympiad
3
$$2(a+b+c)+\frac{9}{(ab+bc+ca)^2}\geq7$$.
$$2(a+b+c)+\frac{9}{(ab+bc+ca)^2}\geq7$$.
Source: 2016 239 S3
October 11, 2020
algebra
inequalities
Problem Statement
Positive real numbers
a
a
a
,
b
b
b
,
c
c
c
are given such that
a
b
c
=
1
abc=1
ab
c
=
1
.Prove that
2
(
a
+
b
+
c
)
+
9
(
a
b
+
b
c
+
c
a
)
2
≥
7.
2(a+b+c)+\frac{9}{(ab+bc+ca)^2}\geq7.
2
(
a
+
b
+
c
)
+
(
ab
+
b
c
+
c
a
)
2
9
≥
7.
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