If \( \alpha \) and \( \beta \) are the distinct roots of the equation \( x^{2}+3^{1 / 4} x \) \... VIDEO
If \( \alpha \) and \( \beta \) are the distinct roots of the equation \( x^{2}+3^{1 / 4} x \) \( +3^{1 / 2}=0 \) then the value of \( \alpha^{96}\left(\alpha^{12}-1\right)+\beta^{96}\left(\beta^{12}-1\right) \) is equal to
(a) \( 56 \times 3^{24} \)
(b) \( 52 \times 3^{24} \)
(c) \( 56 \times 3^{25} \)
(d) \( 28 \times 3^{25} \)
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