Given x = cy + bz; y = az + cx; z = bx + ay where x, y, z are not all zero. The value of a² +b² +c² + 2abc is :

1

− x + cy + bz = 0

cx − y + az = 0

bx + ay − z = 0

since x, y, z are not all zero, using the condition for concurrency

$\left|\begin{array}{ccc}-1 & c & b \\ c & -1 & a \\ b & a & -1\end{array}\right|=0 \Rightarrow-1+2 a b c+a^2+b^2+c^2=0$

$\Rightarrow a^2+b^2+c^2+2 a b c=1$

Hence (1) is the correct answer.