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Mediterranean Mathematics Olympiad
1999 Mediterranean Mathematics Olympiad
4
Brutal Algebra expression
Brutal Algebra expression
Source: Mediterranean MO 1999
October 11, 2012
trigonometry
geometry unsolved
geometry
Problem Statement
In triangle
△
A
B
C
\triangle ABC
△
A
BC
we have
B
C
=
a
,
C
A
=
b
,
A
B
=
c
BC=a,CA=b,AB=c
BC
=
a
,
C
A
=
b
,
A
B
=
c
and
∠
B
=
4
∠
A
\angle B=4\angle A
∠
B
=
4∠
A
Show that
a
b
2
c
3
=
(
b
2
−
a
2
−
a
c
)
(
(
a
2
−
b
2
)
2
−
a
2
c
2
)
ab^2c^3=(b^2-a^2-ac)((a^2-b^2)^2-a^2c^2)
a
b
2
c
3
=
(
b
2
−
a
2
−
a
c
)
((
a
2
−
b
2
)
2
−
a
2
c
2
)
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