9. Let k be a positive integer and let $x_0, x_1, x_2, \cdots$ be an infinite sequence defined by the relationship $$x_0 = 0$$$$x_1 = 1$$$$x_{n+1} = kx_n +x_{n-1}$$For all n $\ge$ 1 (a) For the special case k = 1, prove that $x_{n-1}x_{n+1}$ is never a perfect square for n $\ge$ 2 (b) For the general case of integers k $\ge$ 1, prove that $x_{n-1}x_{n+1}$ is never a perfect square for n $\ge$ 2