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Mathematics
Problem
Let
α
,
β
\alpha, \beta
α
,
β
be the roots of the quadratic equation
x
2
+
6
x
+
3
=
0
x^2 + \sqrt{6}x + 3 = 0
x
2
+
6
x
+
3
=
0
. Then
α
23
+
β
23
+
α
14
+
β
14
α
15
+
β
15
+
α
10
+
β
10
\frac{\alpha^{23} + \beta^{23} + \alpha^{14} + \beta^{14}}{\alpha^{15} + \beta^{15} + \alpha^{10} + \beta^{10}}
α
15
+
β
15
+
α
10
+
β
10
α
23
+
β
23
+
α
14
+
β
14
is (A) 729 (B) 72 (C) 81 (D) 9
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