Period of $f(x-1)+f(x+1)=\sqrt{5}\cdot f(x)$.

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Find the period of: $$f(x-1)+f(x+1)=\sqrt{5}\cdot f(x)\ , \forall x\in R$$

I reduced this down to $f(x-2)+f(x+2)=3f(x)$, I can't get rid off that factor $3$, what to do next, please help.