Let \( p = (x + y + z) \) and \( q = xyz \). If \( \begin{vmatrix} x & 1 & 1 \\ 1 & y & 1 \\ 1 & 1 & z \end{vmatrix} \) is positive, then which one of the following is correct ?
- A. q > p
- B. q + 1 > p
- C. q + 2 > p ✓
- D. q + 2 \ge p
Correct Answer: C. q + 2 > p
Explanation
Expanding the determinant yields xyz - (x + y + z) + 2. Since this must be positive, we get q - p + 2 > 0, which means q + 2 > p.
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