Question

Fibonacci Numbers: Prove that (fn-2)^2 = (fn+1)^2-4(fnfn-1)

Answer 1

Bit lost on how to do this one. I'm starting out with
fn = fn-1 + fn-2 (def of fib)
fn-2 = fn -fn-1 (rearrange)
(fn-2)^2 = (fn+1-fn-1)^2 - 2fnfn-1 +(fn-1)^2
(fn-2)^2 = fn+1^2 -(2fn+1n-2) +fn-1 ^2 -2fn+1fn-1

Answer 2

So if I've done stuff right so far, I need to show that
(fn-1)^2 -2(fn+1fn-1) = -2(fnfn-1)

But I can't see a way to do that? Can someone help out?