Hello! I need to derive Binet's Formula!

I know how to do it for one of the definitions of the Fibonacci sequence: F(1)=1, F(2)=1, F(n)= F(n-1)+ F(n-2), for all n > or = 3.

However, for my assignment, I have to use an alternate definition: F(0)=1, F(1)=1, F(n)= F(n-1)+ F(n-2) for all n > or = 2.

I tried using the same method for the 1st derivation by forming a linear combination and solving for the constants, but I ended up with a formula that doesn't work for n.

Any input would help!