Mathematics

Problem

Let,

\alpha, \beta

be the distinct roots of the equation

x^2 - (t^2 - 5t + 6)x + 1 = 0, t \in \mathbb{R}

and

a_n = \alpha^n + \beta^n

. Then the minimum value of

\frac{a_{2023} + a_{2025}}{a_{2024}}

is \_\_\_\_. (A)

\frac{1}{4}

(B)

-1/2

(C)

-1/4

(D)

1/2