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Given that \((\sqrt{3} - 5\sqrt{2})(\sqrt{3} + \sqrt{2}) = p + q\sqrt{6}\), find q.

Further Mathematics
WAEC 2006

Given that \((\sqrt{3} - 5\sqrt{2})(\sqrt{3} + \sqrt{2}) = p + q\sqrt{6}\), find q.

  • A. 4
  • B. -4
  • C. -5
  • D. -7
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Correct Answer: Option B
Explanation

\((\sqrt{3} - 5\sqrt{2})(\sqrt{3} + \sqrt{2}) = 3 + \sqrt{6} - 5\sqrt{6} - 10\)

= \(-7 - 4\sqrt{6} = p + q\sqrt{6}\)

\(\therefore q = -4\)


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