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Belgium Contests
Flanders Math Olympiad
1993 Flanders Math Olympiad
3
3
Part of
1993 Flanders Math Olympiad
Problems
(1)
inequality (maybe posted before?)
Source: flanders '93
9/27/2005
For
a
,
b
,
c
>
0
a,b,c>0
a
,
b
,
c
>
0
we have:
−
1
<
(
a
−
b
a
+
b
)
1993
+
(
b
−
c
b
+
c
)
1993
+
(
c
−
a
c
+
a
)
1993
<
1
-1 < \left(\dfrac{a-b}{a+b}\right)^{1993} + \left(\dfrac{b-c}{b+c}\right)^{1993} + \left(\dfrac{c-a}{c+a}\right)^{1993} < 1
−
1
<
(
a
+
b
a
−
b
)
1993
+
(
b
+
c
b
−
c
)
1993
+
(
c
+
a
c
−
a
)
1993
<
1
inequalities