MathDB
Problems
Contests
National and Regional Contests
Latvia Contests
Latvia BW TST
2021 Latvia Baltic Way TST
P1
Easy inequality
Easy inequality
Source: Latvian TST for Baltic Way 2021 P1
September 25, 2021
inequalities
Problem Statement
Prove that for positive real numbers
a
,
b
,
c
a,b,c
a
,
b
,
c
satisfying
a
b
c
=
1
abc=1
ab
c
=
1
the following inequality holds:
a
b
(
1
+
c
)
+
b
c
(
1
+
a
)
+
c
a
(
1
+
b
)
≥
3
2
\frac{a}{b(1+c)} +\frac{b}{c(1+a)}+\frac{c}{a(1+b)} \ge \frac{3}{2}
b
(
1
+
c
)
a
+
c
(
1
+
a
)
b
+
a
(
1
+
b
)
c
≥
2
3
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