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1996 Moscow Mathematical Olympiad
1
Moscow 1996 G8 P1 - Is it true that a=b?
Moscow 1996 G8 P1 - Is it true that a=b?
Source:
May 18, 2014
Problem Statement
It is known that
a
+
b
2
a
=
b
+
a
2
b
a+\frac{b^2}{a}=b+\frac{a^2}{b}
a
+
a
b
2
=
b
+
b
a
2
. Is it true that
a
=
b
a=b
a
=
b
, where
a
a
a
and
b
b
b
are nonzero real numbers?Proposed by R.Fedorov
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