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(C) By Newton's sum formula for the equation $x^2 - (t^2 - 5t + 6)x + 1 = 0$,we have:$a_{n+2} - (t^2 - 5t + 6)a_{n+1} + a_n = 0$Rearranging the terms,

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$-1/4$

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(C) By Newton's sum formula for the equation $x^2 - (t^2 - 5t + 6)x + 1 = 0$,we have:$a_{n+2} - (t^2 - 5t + 6)a_{n+1} + a_n = 0$Rearranging the terms,we get:$a_{n+2} + a_n = (t^2 - 5t + 6)a_{n+1}$For $n = 2023$,this becomes:$a_{2025} + a_{2023} = (t^2 - 5t + 6)a_{2024}$Therefore,the ratio is:$\frac{a_{2025} + a_{2023}}{a_{2024}} = t^2 - 5t + 6$To find the minimum value of the quadratic expression $f(t) = t^2 - 5t + 6$,we complete the square:$f(t) = (t - 5/2)^2 - 25/4 + 6 = (t - 5/2)^2 - 1/4$The minimum value occurs at $t = 5/2$,which is $-1/4$.

Let $\alpha$ and $\beta$ be the distinct roots of the equation $x^2 - (t^2 - 5t + 6)x + 1 = 0$,where $t \in \mathbb{R}$,and $a_n = \alpha^n + \beta^n$. Then the minimum value of $\frac{a_{2023} + a_{2025}}{a_{2024}}$ is

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