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Poland - Second Round
1952 Poland - Second Round
4
4
Part of
1952 Poland - Second Round
Problems
(1)
1/ ab +1/ bc +1/ ca =( 1/ ab + bc + ca)
Source: Polish MO second round 1952 p4
8/28/2024
Prove that if the numbers
a
a
a
,
b
b
b
,
c
c
c
satisfy the equation
1
a
b
+
1
b
c
+
1
c
a
=
1
a
b
+
b
c
+
c
a
,
\frac{1}{ab} + \frac{1}{bc} +\frac{1}{ca} = \frac{1}{ab + bc + ca},
ab
1
+
b
c
1
+
c
a
1
=
ab
+
b
c
+
c
a
1
,
then two of them are opposite numbers.
algebra