Given pdf is for

a) Compute the moments about the origin

b) Find the method of moments estimators for a and b (Using a sample of size n).

Attempt:

a)

b) Am i supposed to use part a to find the first and second central moments? I am not sure how to do this. Even so, by looking them up I try the following:

where m1 and m2 are the sample moments.

Basically when I try to solve this system of equations I get gross quadratics that I don't know how to simplify. Is there an elegant way of solving these, or if not, what is the best strategy for attacking these?