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Mathematics
Mathematics
Problem
If
α
\alpha
α
,
β
\beta
β
,
γ
\gamma
γ
are the roots of the cubic
2010
x
3
+
4
x
2
+
1
=
0
2010x^3 + 4x^2 + 1 = 0
2010
x
3
+
4
x
2
+
1
=
0
, then the value of
(
α
−
2
+
β
−
2
+
γ
−
2
)
(\alpha^{-2} + \beta^{-2} + \gamma^{-2})
(
α
−
2
+
β
−
2
+
γ
−
2
)
is equal to
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