For an=an−1+an−2a_n = a_{n-1} + a_{n-2}an=an−1+an−2, what is the relation between FnF_nFn and the roots ϕ,ψ\phi, \psiϕ,ψ?
Fn=ϕn−ψn5F_n = \frac{\phi^n - \psi^n}{\sqrt{5}}Fn=5ϕn−ψn
Fn=ϕn+ψn5F_n = \frac{\phi^n + \psi^n}{\sqrt{5}}Fn=5ϕn+ψn
Fn=ϕn−ψnF_n = \phi^n - \psi^nFn=ϕn−ψn
Fn=ϕn−ψn2F_n = \frac{\phi^n - \psi^n}{2}Fn=2ϕn−ψn