2016/075) derive the following given $u_n$ the $n^{th}$ fibonacci number $u_{n+1}^2 - 4u_nu_{n-1} = u_{n-2}^2$

we have
$u_{n+1}^2 -  u_{n-2}^2$
$= (u_n + u_{n-1})^2 -  (u_n - u_{n-1})^2$
$=4u_nu_{n-1}$ using $(a+b)^2 - (a-b)^2 = 4ab$
hence $u_{n+1}^2 - 4u_nu_{n-1} = u_{n-2}^2$