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National and Regional Contests
China Contests
(China) National High School Mathematics League
2014 China Second Round Olympiad
1
1
Part of
2014 China Second Round Olympiad
Problems
(1)
China Second Round Olympiad 2014 Second Part Problem 1
Source: 14 Sep 2014
9/14/2014
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be real numbers such that
a
+
b
+
c
=
1
a+b+c=1
a
+
b
+
c
=
1
and
a
b
c
>
0
abc>0
ab
c
>
0
. Prove that
b
c
+
c
a
+
a
b
<
a
b
c
2
+
1
4
.
bc+ca+ab<\frac{\sqrt{abc}}{2}+\frac{1}{4}.
b
c
+
c
a
+
ab
<
2
ab
c
+
4
1
.
inequalities proposed
inequalities
China
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