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MathLinks Contest 6th
4.3
0643 radical inequality 6th edition Round 4 p3
0643 radical inequality 6th edition Round 4 p3
Source:
May 3, 2021
inequalities
6th edition
Problem Statement
Let
a
,
b
,
c
a, b, c
a
,
b
,
c
be positive real numbers such that
a
b
c
=
1
abc = 1
ab
c
=
1
. Prove that
a
+
b
b
+
1
+
b
+
c
c
+
1
+
c
+
a
a
+
1
≥
3
\sqrt{\frac{a+b}{b+1}}+\sqrt{\frac{b+c}{c+1}}+\sqrt{\frac{c+a}{a+1}} \ge 3
b
+
1
a
+
b
+
c
+
1
b
+
c
+
a
+
1
c
+
a
≥
3
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