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IMO Longlists
1985 IMO Longlists
79
If the first identity holds, so on the second
If the first identity holds, so on the second
Source:
September 14, 2010
algebra
polynomial
algebra solved
Problem Statement
Let
a
,
b
a, b
a
,
b
, and
c
c
c
be real numbers such that
1
b
c
−
a
2
+
1
c
a
−
b
2
+
1
a
b
−
c
2
=
0.
\frac{1}{bc-a^2} + \frac{1}{ca-b^2}+\frac{1}{ab-c^2} = 0.
b
c
−
a
2
1
+
c
a
−
b
2
1
+
ab
−
c
2
1
=
0.
Prove that
a
(
b
c
−
a
2
)
2
+
b
(
c
a
−
b
2
)
2
+
c
(
a
b
−
c
2
)
2
=
0.
\frac{a}{(bc-a^2)^2} + \frac{b}{(ca-b^2)^2}+\frac{c}{(ab-c^2)^2} = 0.
(
b
c
−
a
2
)
2
a
+
(
c
a
−
b
2
)
2
b
+
(
ab
−
c
2
)
2
c
=
0.
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