Question

lf `alpha and beta` are the roots of the equation `x^2-ax + b = 0 and A_n = alpha^n + beta^n`, then which of the following is true ?
A. `A_(n+1) = a A_(n) + b A_(n-1)`
B. `A_(n+1) = b A_(n) + a A_(n-1)`
C. `A_(n+1) = a A_(n) - b A_(n-1)`
D. `A_(n+1) = b A_(n) - a A_(n-1)`

Answer 1

Correct Answer - C

Answer 2

https://www.sarthaks.com/?qa=blob&qa_blobid=15976319048135211351

x² – ax + b = 0

α and β are roots then

α² - aα + b = 0

Multiply with α^n-1 then

αⁿ⁺¹ - aαⁿ + bα^n-1 = 0 ........(i)

Similarly

βⁿ⁺¹ - αβⁿ + bβ^n-1 = 0 ........(ii)

Adding Eqn (i) and (ii)