Multiple choice general knowledge math & puzzles

Let a, b, c be any real numbers. Suppose that there are nubers 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

  1. 0

  2. 1

  3. 2

  4. -2
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B Correct answer
AI explanation

Adding the three equations and manipulating them algebraically (multiplying appropriately by x, y, z and combining) leads to the identity a² + b² + c² + 2abc = 1, a known result for this classic system when x, y, z are not all zero. This is a standard competition-style algebra identity rather than something solved by picking arbitrary numbers, and it holds regardless of the specific nonzero values of x, y, z.

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