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Junior Regional - Federation of Bosnia Herzegovina
2015 Junior Regional Olympiad - FBH
2
Junior Regional Olympiad - FBH 2015 Grade 8 Problem 2
Junior Regional Olympiad - FBH 2015 Grade 8 Problem 2
Source:
October 1, 2018
value
Problem Statement
Show tha value
A
=
(
b
−
c
)
2
(
a
−
b
)
(
a
−
c
)
+
(
c
−
a
)
2
(
b
−
c
)
(
b
−
a
)
+
(
a
−
b
)
2
(
c
−
a
)
(
c
−
b
)
A=\frac{(b-c)^2}{(a-b)(a-c)}+\frac{(c-a)^2}{(b-c)(b-a)}+\frac{(a-b)^2}{(c-a)(c-b)}
A
=
(
a
−
b
)
(
a
−
c
)
(
b
−
c
)
2
+
(
b
−
c
)
(
b
−
a
)
(
c
−
a
)
2
+
(
c
−
a
)
(
c
−
b
)
(
a
−
b
)
2
does not depend on values of
a
a
a
,
b
b
b
and
c
c
c
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