We will find the solution to the following lhcc recurrence: an=8an−1−16an−2 for n≥2 with initial conditions a0=4,a1=7. the first step as usual is to find the characteristic equation by trying a solution of the "geometric" format an=rnan=rn. (we assume also r≠0). in this case we get: rn=8r^n−1−16r^n−2. since we are assuming r≠0r≠0 we can divide by the smallest power of r, i. e., rn−2 to get the characteristic equation:

r^2=8r−16. (notice since our lhcc recurrence was degree 2, the characteristic equation is degree 2.)

this characteristic equation has a single root rr. (we say the root has multiplicity 2). find r.
r=?