Question

Given, x = cy + bz, y = az + cx, z = bx + ay, where x, y, z are not all zero, prove that a² + b² + c² + 2ab = 1.

Answer 1

 Given systems of equations can be rewritten as

Above system of equations are homogeneous equation. Since, x, y and z arc not all zero, so it has non-trivial solution.

Therefore, the coefficient of determinant must be zero.