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National and Regional Contests
Russia Contests
Saint Petersburg Mathematical Olympiad
2019 Saint Petersburg Mathematical Olympiad
3
Simple inequality
Simple inequality
Source: St. Petersburg Mathematical Olympiad 2019
April 13, 2019
inequalities
Problem Statement
Let
a
,
b
a, b
a
,
b
and
c
c
c
be non-zero natural numbers such that
c
≥
b
c \geq b
c
≥
b
. Show that
a
b
(
a
+
b
)
c
>
c
b
a
c
.
a^b\left(a+b\right)^c>c^b a^c.
a
b
(
a
+
b
)
c
>
c
b
a
c
.
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