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2016 Kyrgyzstan National Olympiad
1
a+b+c=0,then?
a+b+c=0,then?
Source: Kyrgyzstan national 2016 1-problem
May 10, 2016
algebra
Problem Statement
If
a
+
b
+
c
=
0
a+b+c=0
a
+
b
+
c
=
0
,then find the value of
(
a
b
−
c
+
b
c
−
a
+
c
a
−
b
)
(
b
−
c
a
+
c
−
a
b
+
a
−
b
c
)
(\frac{a}{b-c}+\frac{b}{c-a}+\frac{c}{a-b})(\frac{b-c}{a}+\frac{c-a}{b}+\frac{a-b}{c})
(
b
−
c
a
+
c
−
a
b
+
a
−
b
c
)
(
a
b
−
c
+
b
c
−
a
+
c
a
−
b
)
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