F5 Maths question

ax + cy + bz = 0...(1)
cx + by + az = 0...(2)
bx + ay + cz = 0...(3)

As (0,0,0) is one solution of the system. If there is another solution rather than (0,0,0), then there are infinite solutions of the system.

This implies that the determinant of the system is 0

| a c b |
| c b a | = 0
| b a c |

=> a^2 + b^2 + c^3 = 3abc