MathDB
Problems
Contests
International Contests
JBMO ShortLists
2018 JBMO Shortlist
A6
A6
Part of
2018 JBMO Shortlist
Problems
(1)
JBMO shortlist 2018 inequality
Source: JBMO shortlist
6/23/2019
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
Inequality
algebra
inequalities