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Baltic Way
2005 Baltic Way
5
5
Part of
2005 Baltic Way
Problems
(1)
inequality with abc=1
Source: Serbia & Montenegro ST 2005 problem 5; Baltic Way 2005/5
6/1/2005
Let
a
a
a
,
b
b
b
,
c
c
c
be positive real numbers such that
a
b
c
=
1
abc=1
ab
c
=
1
. Prove that
a
a
2
+
2
+
b
b
2
+
2
+
c
c
2
+
2
≤
1
\frac a{a^{2}+2}+\frac b{b^{2}+2}+\frac c{c^{2}+2}\leq 1
a
2
+
2
a
+
b
2
+
2
b
+
c
2
+
2
c
≤
1
inequalities
logarithms
inequalities proposed