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2011 Indonesia MO
7
7
Part of
2011 Indonesia MO
Problems
(1)
Decrementing the power
Source: Indonesian Mathematics Olympiad 2011, Day 2, Problem 7
9/14/2011
Let
a
,
b
,
c
∈
R
+
a,b,c \in \mathbb{R}^+
a
,
b
,
c
∈
R
+
and
a
b
c
=
1
abc = 1
ab
c
=
1
such that
a
2011
+
b
2011
+
c
2011
<
1
a
2011
+
1
b
2011
+
1
c
2011
a^{2011} + b^{2011} + c^{2011} < \dfrac{1}{a^{2011}} + \dfrac{1}{b^{2011}} + \dfrac{1}{c^{2011}}
a
2011
+
b
2011
+
c
2011
<
a
2011
1
+
b
2011
1
+
c
2011
1
. Prove that
a
+
b
+
c
<
1
a
+
1
b
+
1
c
a + b + c < \dfrac{1}{a} + \dfrac{1}{b} + \dfrac{1}{c}
a
+
b
+
c
<
a
1
+
b
1
+
c
1
.
inequalities proposed
inequalities