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Bangladesh Contests
Bangladesh Mathematical Olympiad
2024 Bangladesh Mathematical Olympiad
P3
Find the value
Find the value
Source: BdMO 2024 Secondary National P3
March 18, 2024
algebra
equation
Problem Statement
Let
a
a
a
and
b
b
b
be real numbers such that
a
a
2
−
5
=
b
5
−
b
2
=
a
b
a
2
b
2
−
5
\frac{a}{a^2-5} = \frac{b}{5-b^2} = \frac{ab}{a^2b^2-5}
a
2
−
5
a
=
5
−
b
2
b
=
a
2
b
2
−
5
ab
where
a
+
b
≠
0
a+b \neq 0
a
+
b
=
0
.
a
4
+
b
4
=
a^4 + b^4 =
a
4
+
b
4
=
?
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