If \( \alpha \), \( \beta \), \( \gamma \) are cube roots of -8, then what is \( \frac{\alpha^2 p^2 + \beta^2 q^2 + \gamma^2 r^2}{\beta^2 p^2 + \gamma^2 q^2 + \alpha^2 r^2} \) equal to ?

  1. A. \frac{\gamma}{\alpha}
  2. B. \frac{\gamma}{\beta}
  3. C. \frac{2\gamma}{\alpha}
  4. D. \frac{2\gamma}{\beta}

Correct Answer: B. \frac{\gamma}{\beta}

Explanation

The cube roots of -8 are -2, -2\omega, -2\omega^2. Substituting these into the expression and simplifying yields \omega, which matches the ratio \gamma/\beta.

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