The problem is here. Now I know the definition of mixed/max/min phase wavelets, whether the roots lie within the unit circle or not. Starting from n = 1, let $$ x_t = ( 5, 6) $$ $$ X(z) = 5 + 6z $$ This would have root -5/6, making it a max phase wavelet (since it's within unit circle). If we switch 5 and 6 around in xt, we would get root -6/5, which would make it a min phase wavelet.
I don't know how I would show they have same amplitude spectrum. I know |X(f)| amplitude spectrum would lie between -fc and fc (Nyquist frequency) and fc = 1/2*delta t. Not sure how I would go about proving it.