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Jozsef Wildt International Math Competition
2019 Jozsef Wildt International Math Competition
W. 36
Prove this inequalitiy 2
Prove this inequalitiy 2
Source: 2019 Jozsef Wildt International Math Competition-W. 36
May 19, 2020
inequalities
Problem Statement
For any
a
a
a
,
b
b
b
,
c
>
0
c > 0
c
>
0
and for any
n
∈
N
∗
n \in \mathbb{N}^*
n
∈
N
∗
, prove the inequality
(
a
−
b
)
(
a
b
)
n
+
(
b
−
c
)
(
b
c
)
n
+
(
c
−
a
)
(
c
a
)
n
≥
(
a
−
b
)
a
b
+
(
b
−
c
)
b
c
+
(
c
−
a
)
c
a
(a - b)\left(\frac{a}{b}\right)^n+(b - c)\left(\frac{b}{c}\right)^n+(c - a)\left(\frac{c}{a}\right)^n\geq (a - b)\frac{a}{b}+(b - c)\frac{b}{c}+(c - a)\frac{c}{a}
(
a
−
b
)
(
b
a
)
n
+
(
b
−
c
)
(
c
b
)
n
+
(
c
−
a
)
(
a
c
)
n
≥
(
a
−
b
)
b
a
+
(
b
−
c
)
c
b
+
(
c
−
a
)
a
c
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