Question

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 and z = bx + ay. Then a² + b² + c² + 2abc is equal to
(a) 1 

(b) 2 

(c) – 1 

(d) 0

Answer 1

(a) : System of equations

x – cy – bz = 0

cx – y + az = 0

bx + ay – z = 0
has non trivial solution if the determinant of coefficient matrix is zero