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Let a, b, c be real numbers. Suppose there exist real numbers x, y, z, not all zero, such that x = c*y + b*z, y = a*z + c*x and z = b*x + a*y. Then the value of a² + b² + c² + 2*a*b*c equals

1. 2
2. -1
3. 0
4. 1

Correct answer: 1

Solution

The condition for non-trivial (x, y, z) is that the determinant of the system vanishes, and expanding it gives 1 - (a² + b² + c² + 2abc) = 0.

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