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Mathematics
Mathematics
Problem
The equation
x
2
+
b
x
+
c
=
0
x^2 + bx + c = 0
x
2
+
b
x
+
c
=
0
has distinct roots. If 2 is subtracted from each root, the results are reciprocals of the original roots. The value of
(
b
2
+
c
2
+
b
c
)
(b^2 + c^2 + bc)
(
b
2
+
c
2
+
b
c
)
equals
x
2
+
b
x
+
c
=
0
α
x^2 + bx + c = 0 \quad \alpha
x
2
+
b
x
+
c
=
0
α
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