I am having trouble starting this question.
Given that the sequence ($x_n$) satisfies the recurrence relation:
$x_n$$_+$$_1$ = a$x_n$ + b$x_n$$_−$$_1$, where $n= 1, 2, ...$ and $a$ and $b$ are given numbers.
If the quadratic $r^2-ar-b = 0$ has distinct roots $\alpha$ and $\beta$,
show that $x_n$ = $\alpha^n$ and $x_n$ = $\beta^n$ are both solutions of the recurrence relation shown above.
I have looked at this so many times and wherever I start I get nowhere, thanks for any help in advance.