Mathematics

Problem

Let

\alpha, \beta

and

x

be the roots of the equation

x^3 - 4x + 1 = 0

. If

T_n = \alpha^n + \beta^n + x^n

n \geq 1

, then which of the following is (are) true? [Note:

[x]

denotes greatest integer function less than or equal to

x

.] (A)

T_6 - 4T_4 = 3

(B)

T_{96} + 2T_{99} + T_{102} = 16T_{98}

(C)

T_{96} + 2T_{99} + T_{102} = 16T_{100}

(D)

[\alpha] + [\beta] + [x] = 2