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1990 Greece National Olympiad
2
a/(b^3-1)+b/(a^3-1)=2(ab-2)/ (a^2b^2+3) 1990 Greece MO Grade X p2
a/(b^3-1)+b/(a^3-1)=2(ab-2)/ (a^2b^2+3) 1990 Greece MO Grade X p2
Source:
September 6, 2024
algebra
Problem Statement
If
a
+
b
=
1
a+b=1
a
+
b
=
1
,
∈
R
\in \mathbb{R}
∈
R
and
a
b
≠
0
ab \ne 0
ab
=
0
, prove that
a
b
3
−
1
+
b
a
3
−
1
=
2
(
a
b
−
2
)
a
2
b
2
+
3
\frac{a}{b^3-1}+\frac{b}{a^3-1}=\frac{2(ab-2)}{a^2b^2+3}
b
3
−
1
a
+
a
3
−
1
b
=
a
2
b
2
+
3
2
(
ab
−
2
)
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