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Austrian-Polish
1985 Austrian-Polish Competition
1
A+b+c=0
A+b+c=0
Source: Lithuanian Mathematical Olympiad 2006
April 12, 2006
inequalities
algebra unsolved
algebra
Problem Statement
Show that if
a
+
b
+
c
=
0
a+b+c=0
a
+
b
+
c
=
0
then
(
a
b
−
c
+
b
c
−
a
+
c
a
−
b
)
(
b
−
c
a
+
c
−
a
b
+
a
−
b
c
)
=
9
(\frac{a}{b-c}+\frac{b}{c-a}+\frac{c}{a-b})(\frac{b-c}{a}+\frac{c-a}{b}+\frac{a-b}{c})=9
(
b
−
c
a
+
c
−
a
b
+
a
−
b
c
)
(
a
b
−
c
+
b
c
−
a
+
c
a
−
b
)
=
9
.
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