periodicity of function If $f(x+1) + f(x-1) = \sqrt3f(x)$, then what is the period of $f(x)$?

$$ f(x+1)+f(x-1) = \sqrt{3} f(x) $$ 
$$ \sqrt{3}f(x+1) + \sqrt{3}f(x-1)= 3f(x) $$ 
$$ f(x)+f(x+2)+f(x-2)+f(x)= 3 f(x)$$
$$ f(x+2)+f(x-2)=f(x) $$ 
$$ f(x+4)+f(x) = f(x+2) $$ 
Adding last two equations give , 
$$ f(x+4)+f(x-2)= 0$$ 
$$ f(x+10)+f(x+4)= 0 \implies f(x+10) = f(x-2) \implies f(x+12)=f(x) $$ 
Thus period = 12 $\Box$
