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German National Olympiad
2010 German National Olympiad
2
cyclic with pairwise distinct a,b,c. Strange equality cases
cyclic with pairwise distinct a,b,c. Strange equality cases
Source: german math olympiad 2010
June 7, 2011
inequalities unsolved
inequalities
Problem Statement
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be pairwise distinct real numbers. Show that
(
2
a
−
b
a
−
b
)
2
+
(
2
b
−
c
b
−
c
)
2
+
(
2
c
−
a
c
−
a
)
2
≥
5.
(\frac{2a-b}{a-b})^2+(\frac{2b-c}{b-c})^2+(\frac{2c-a}{c-a})^2 \ge 5.
(
a
−
b
2
a
−
b
)
2
+
(
b
−
c
2
b
−
c
)
2
+
(
c
−
a
2
c
−
a
)
2
≥
5.
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