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All-Russian Olympiad Regional Round
2009 All-Russian Olympiad Regional Round
9.2
9.2
Part of
2009 All-Russian Olympiad Regional Round
Problems
(1)
1-ab=rational^2 if a^3b+ab^3+2a^2b2+2a + 2b + 1 = 0
Source: All-Russian MO 2009 Regional 9.2
8/27/2024
Rational numbers
a
a
a
and
b
b
b
satisfy the equality
a
3
b
+
a
b
3
+
2
a
2
b
2
+
2
a
+
2
b
+
1
=
0.
a^3b+ab^3+2a^2b^2+2a + 2b + 1 = 0.
a
3
b
+
a
b
3
+
2
a
2
b
2
+
2
a
+
2
b
+
1
=
0.
Prove that the number
1
ā
a
b
1-ab
1
ā
ab
is the square of the rational numbers.
algebra
Perfect Square