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Lusophon Mathematical Olympiad
2019 Lusophon Mathematical Olympiad
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Part of
2019 Lusophon Mathematical Olympiad
Problems
(1)
2(a^2 + 1)(b^2 + 1) = (a + 1)(b + 1)(ab + 1) in R
Source: Lusophon 2019 CPLP P4
12/31/2019
Find all the real numbers
a
a
a
and
b
b
b
that satisfy the relation
2
(
a
2
+
1
)
(
b
2
+
1
)
=
(
a
+
1
)
(
b
+
1
)
(
a
b
+
1
)
2(a^2 + 1)(b^2 + 1) = (a + 1)(b + 1)(ab + 1)
2
(
a
2
+
1
)
(
b
2
+
1
)
=
(
a
+
1
)
(
b
+
1
)
(
ab
+
1
)
algebra
equation