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If x² + y² + z² = 3, where x, y and z are integers, then how many values can (xy + yz + zx) have?

This question was previously asked in
CDS 2 2025 Maths Question Paper (14-Sep-2025)
The correct answer is

Two

Given x² + y² + z² = 3. Since x, y, z are integers, the possible values are: (1, 1, 1), (1, -1, 1), (1, 1, -1), (1, -1, -1), (-1, 1, 1), (-1, -1, 1), (-1, 1, -1), (-1, -1, -1) If (x, y, z) = (1, 1, 1), xy + yz + zx = 3 If (x, y, z) = (1, 1, -1), xy + yz + zx = 1 - 1 - 1 = -1 If (x, y, z) = (1, -1, -1), xy + yz + zx = -1 + 1 -1 = -1 If (x, y, z) = (-1, -1, -1), xy + yz + zx = -3

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