Express \(\frac{2}{3 - \sqrt{7}} \text{ in the form} a + \sqrt{b}\), where a and b...
FURTHER MATHEMATICS
WAEC 2009
Express \(\frac{2}{3 - \sqrt{7}} \text{ in the form} a + \sqrt{b}\), where a and b are integers.
- A. \(6 + \sqrt{7}\)
- B. \(3 + \sqrt{7}\)
- C. \(3 - \sqrt{7}\)
- D. \(6 - \sqrt{7}\)
Correct Answer: B. \(3 + \sqrt{7}\)
Explanation
Rationalizing \(\frac{2}{3 - \sqrt{7}}\) by multiplying through with \(3 + \sqrt{7}\),
\(\frac{2}{3 - \sqrt{7}} \frac{(3 + \sqrt{7})}{(3 + \sqrt{7})} = \frac{6 + 2\sqrt{7}}{9 - 7}\)
= \(\frac{6 + 2\sqrt{7}}{2} = 3 + \sqrt{7}\)
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