If the system of equations x=cy+bz,y=az+cx,z=bx+ay  has a nonzero solution then  a2+b2+c2+2abc=

x=cy+bz,y=az+cx,z=bx+ay⇒−1cbc−1aba−1xyz=000 Given equations has non zero solution ⇒−1cbc−1aba−1=0⇒−11−a2−c(−1−ab)+b(ac+b)=0⇒−1+a2+c2+abc+abc+b2=0⇒a2+b2+c2+2abc=1