MathDB
Problems
Contests
International Contests
JBMO ShortLists
2019 JBMO Shortlist
A6
JBMO Shortlist 2019 A6
JBMO Shortlist 2019 A6
Source:
September 12, 2020
algebra
inequalities
JBMO
Problem Statement
Let
a
,
b
,
c
a, b, c
a
,
b
,
c
be positive real numbers. Prove the inequality
(
a
2
+
a
c
+
c
2
)
(
1
a
+
b
+
c
+
1
a
+
c
)
+
b
2
(
1
b
+
c
+
1
a
+
b
)
>
a
+
b
+
c
(a^2+ac+c^2) \left( \frac{1}{a+b+c}+\frac{1}{a+c} \right)+b^2 \left( \frac{1}{b+c}+\frac{1}{a+b} \right)>a+b+c
(
a
2
+
a
c
+
c
2
)
(
a
+
b
+
c
1
+
a
+
c
1
)
+
b
2
(
b
+
c
1
+
a
+
b
1
)
>
a
+
b
+
c
.Proposed by Tajikistan
Back to Problems
View on AoPS