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Mathematics
Mathematics
Problem
Let
α
,
β
,
γ
,
δ
\alpha, \beta, \gamma, \delta
α
,
β
,
γ
,
δ
be four roots of the eqn.
x
4
−
4
x
3
+
5
x
2
−
2
x
−
2
=
0
x^4 - 4x^3 + 5x^2 - 2x - 2 = 0
x
4
−
4
x
3
+
5
x
2
−
2
x
−
2
=
0
. If the value of
1
(
α
2
−
2
α
+
3
)
2
+
1
(
β
2
−
2
β
+
3
)
2
+
1
(
γ
2
−
2
γ
+
3
)
2
+
1
(
δ
2
−
2
δ
+
3
)
2
\frac{1}{(\alpha^2 - 2\alpha + 3)^2} + \frac{1}{(\beta^2 - 2\beta + 3)^2} + \frac{1}{(\gamma^2 - 2\gamma + 3)^2} + \frac{1}{(\delta^2 - 2\delta + 3)^2}
(
α
2
−
2
α
+
3
)
2
1
+
(
β
2
−
2
β
+
3
)
2
1
+
(
γ
2
−
2
γ
+
3
)
2
1
+
(
δ
2
−
2
δ
+
3
)
2
1
is
a
b
\frac{a}{b}
b
a
, (where
a
,
b
a, b
a
,
b
are coprime numbers), then the value of
(
a
−
b
)
(a-b)
(
a
−
b
)
is: (A) 4 (B) 7 (C) 1 (D) 9
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