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Baltic Way
2020 Baltic Way
2
2
Part of
2020 Baltic Way
Problems
(1)
Cyclic inequality with fractions and roots
Source: Baltic Way 2020, Problem 2
11/14/2020
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
1
a
c
2
+
1
+
1
b
a
2
+
1
+
1
c
b
2
+
1
>
2.
\frac{1}{a\sqrt{c^2 + 1}} + \frac{1}{b\sqrt{a^2 + 1}} + \frac{1}{c\sqrt{b^2+1}} > 2.
a
c
2
+
1
1
+
b
a
2
+
1
1
+
c
b
2
+
1
1
>
2.
inequalities
inequalities proposed
cyclic inequality
algebra