Prove that \[(x^{2} +xy -y^{2})^{2}=1\] has consecutive Fibonacci numbers as solution

Question

Apologies if it's a duplicate question. I was not able to find such question though. I don't know how to proceed on this.

Answer 1

The hint.

Prove by induction that $$f_{n+1}^2-f_{n+1}f_n-f_n^2=(-1)^n.$$