discrete mathematics - Mathematical induction on Lucas sequence and Fibonacci sequence

I'm trying to prove the following:
$$L_k^2-5F_k^2=4(-1)^k\qquad k\ge1$$

$L_k$ is the $k$th term of the Lucas numbers and $F_k$ is the $k$th term of the Fibonacci sequence.

I've tried using mathematical induction, however it's not working out too well. I tried starting out by manipulating $L^2_{k+1}-5F^2_{k+1}$, but I can't prove that it equals $4(-1)^{k+1}$.

Any help is greatly appreciated!