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Mathematics
Mathematics
Problem
If
α
+
1
α
\alpha + \frac{1}{\alpha}
α
+
α
1
and
2
−
β
−
1
β
2 - \beta - \frac{1}{\beta}
2
−
β
−
β
1
, (
α
,
β
>
0
\alpha, \beta > 0
α
,
β
>
0
) are the roots of the quadratic equation
x
2
−
2
(
a
+
1
)
x
+
a
−
3
=
0
x^2 - 2(a+1)x + a - 3 = 0
x
2
−
2
(
a
+
1
)
x
+
a
−
3
=
0
, then find the sum of integral values of
a
a
a
.
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