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National and Regional Contests
China Contests
(China) National High School Mathematics League
2015 China Second Round Olympiad
1
China Second Round Olympiad 2015 （B) Test 2 ，Q1
China Second Round Olympiad 2015 （B) Test 2 ，Q1
Source: Sep 13, 2015
September 15, 2015
inequalities
Problem Statement
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be nonnegative real numbers.Prove that
(
a
−
b
c
)
2
+
(
b
−
c
a
)
2
+
(
c
−
a
b
)
2
(
a
−
b
)
2
+
(
b
−
c
)
2
+
(
c
−
a
)
2
≥
1
2
.
\frac{(a-bc)^2+(b-ca)^2+(c-ab)^2}{(a-b)^2+(b-c)^2+(c-a)^2}\geq\frac{1}{2}.
(
a
−
b
)
2
+
(
b
−
c
)
2
+
(
c
−
a
)
2
(
a
−
b
c
)
2
+
(
b
−
c
a
)
2
+
(
c
−
ab
)
2
≥
2
1
.
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