Let $a,b,c$ be any real numbers. Suppose that there are real numbers $x,y,z$ not all zero. Such that $x=cy+bz,y=az+cx,z=bx+ay$. Then $a^2+b^2+2abc$ is equal to

Question

$(a)\;2\qquad(b)\;-1\qquad(c)\;0\qquad(d)\;1$