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Serbia Contests
Serbia Team Selection Test
2005 Serbia Team Selection Test
5
simple ineq....
simple ineq....
Source: Serbia IMO TST 2005
May 23, 2016
inequalities
Problem Statement
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be positive reals such that
a
b
c
=
1
abc=1
ab
c
=
1
.Prove the inequality
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
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