MathDB
Problems
Contests
National and Regional Contests
Latvia Contests
Latvia BW TST
2021 Latvia Baltic Way TST
P1
P1
Part of
2021 Latvia Baltic Way TST
Problems
(1)
Easy inequality
Source: Latvian TST for Baltic Way 2021 P1
9/25/2021
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
inequalities