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Regional Mathematical Olympiad
2016 India Regional Mathematical Olympiad
2
Algebra Inequality
Algebra Inequality
Source: RMO 2016 Karnataka Region P2
October 16, 2016
inequalities
Problem Statement
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be three distinct positive real numbers such that
a
b
c
=
1
abc=1
ab
c
=
1
. Prove that
a
3
(
a
−
b
)
(
a
−
c
)
+
b
3
(
b
−
c
)
(
b
−
a
)
+
c
3
(
c
−
a
)
(
c
−
b
)
≥
3
\dfrac{a^3}{(a-b)(a-c)}+\dfrac{b^3}{(b-c)(b-a)}+\dfrac{c^3}{(c-a)(c-b)} \ge 3
(
a
−
b
)
(
a
−
c
)
a
3
+
(
b
−
c
)
(
b
−
a
)
b
3
+
(
c
−
a
)
(
c
−
b
)
c
3
≥
3
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