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National and Regional Contests
Russia Contests
239 Open Math Olympiad
2011 239 Open Mathematical Olympiad
7
7
Part of
2011 239 Open Mathematical Olympiad
Problems
(1)
(ab+bc+ca+1)(a+b)(b+c)(c+a) \ge 2abc(a+b+c+1)^2
Source: 239 2011 J7
5/18/2020
Prove for positive reals
a
,
b
,
c
a,b,c
a
,
b
,
c
that
(
a
b
+
b
c
+
c
a
+
1
)
(
a
+
b
)
(
b
+
c
)
(
c
+
a
)
≥
2
a
b
c
(
a
+
b
+
c
+
1
)
2
(ab+bc+ca+1)(a+b)(b+c)(c+a) \ge 2abc(a+b+c+1)^2
(
ab
+
b
c
+
c
a
+
1
)
(
a
+
b
)
(
b
+
c
)
(
c
+
a
)
≥
2
ab
c
(
a
+
b
+
c
+
1
)
2
inequalities