Let , be the distinct roots of the equation x^2- (t^2-5 t+6 ) x+1=0, t R and a_n= ^n+ ^n . Then the minimum value of a₂₀₂₃+a₂₀₂₅ a₂₀₂₄ is

Step-by-step solution

by newton's theorem aligned & a _ n +2 - ( t ^2-5 t +6 ) a _ n +1 + a _ n =0 & a ₂₀₂₅+ a ₂₀₂₃= ( t ^2-5 t +6 ) a ₂₀₂₄ & a ₂₀₂₅+ a ₂₀₂₃ a ₂₀₂₄ = t ^2-5 t +6 & t ^2-5 t +6= ( t - 5 2 )^2- 1 4 & minimum value =- 1 4 aligned