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JBMO ShortLists
2018 JBMO Shortlist
A6
JBMO shortlist 2018 inequality
JBMO shortlist 2018 inequality
Source: JBMO shortlist
June 23, 2019
Inequality
algebra
inequalities
Problem Statement
For
a
,
b
,
c
a,b,c
a
,
b
,
c
positive real numbers such that
a
b
+
b
c
+
c
a
=
3
ab+bc+ca=3
ab
+
b
c
+
c
a
=
3
, prove:
a
a
3
+
5
+
b
b
3
+
5
+
c
c
3
+
5
≤
6
2
\frac{a}{\sqrt{a^3+5}}+\frac{b}{\sqrt{b^3+5}}+\frac{c}{\sqrt{c^3+5}} \leq \frac{\sqrt{6}}{2}
a
3
+
5
a
+
b
3
+
5
b
+
c
3
+
5
c
≤
2
6
Proposed by Dorlir Ahmeti, Albania
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