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National and Regional Contests
Indonesia Contests
Indonesia MO Shortlist
2015 Indonesia MO Shortlist
A3
Inequality....
Inequality....
Source: INAMO Shortlist 2015
April 7, 2019
Inequality
inequalities
Problem Statement
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
positive reals such that
a
2
+
b
2
+
c
2
=
1
a^2+b^2+c^2=1
a
2
+
b
2
+
c
2
=
1
. Prove that
a
+
b
a
b
+
1
+
b
+
c
b
c
+
1
+
c
+
a
a
c
+
1
≤
3
\frac{a+b}{\sqrt{ab+1}}+\frac{b+c}{\sqrt{bc+1}}+\frac{c+a}{\sqrt{ac+1}}\le 3
ab
+
1
a
+
b
+
b
c
+
1
b
+
c
+
a
c
+
1
c
+
a
≤
3
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