Let α, β be the distinct roots of the equation x^2-(t^2-5 t+6) x+1=0, t ∈ R and a_n=α^n+β^n. Then the minimum value of (a_2023+a_2025)/(a_2024) is

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