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239 Open Math Olympiad
2017 239 Open Mathematical Olympiad
7
extremum inequality with \frac{1}{a+b} and \frac{1}{a^2+bc}
extremum inequality with \frac{1}{a+b} and \frac{1}{a^2+bc}
Source: 239 2017 J7
June 3, 2020
Inequality
inequalities
Problem Statement
Find the greatest possible value of
s
>
0
s>0
s
>
0
, such that for any positive real numbers
a
,
b
,
c
a,b,c
a
,
b
,
c
,
(
1
a
+
b
+
1
b
+
c
+
1
c
+
a
)
2
≥
s
(
1
a
2
+
b
c
+
1
b
2
+
c
a
+
1
c
2
+
a
b
)
.
(\frac{1}{a+b}+\frac{1}{b+c}+\frac{1}{c+a})^2 \geq s(\frac{1}{a^2+bc}+\frac{1}{b^2+ca}+\frac{1}{c^2+ab}).
(
a
+
b
1
+
b
+
c
1
+
c
+
a
1
)
2
≥
s
(
a
2
+
b
c
1
+
b
2
+
c
a
1
+
c
2
+
ab
1
)
.
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