WAEC - Further Mathematics (2009 - No. 8)
Express \(\frac{2}{3 - \sqrt{7}} \text{ in the form} a + \sqrt{b}\), where a and b are integers.
\(6 + \sqrt{7}\)
\(3 + \sqrt{7}\)
\(3 - \sqrt{7}\)
\(6 - \sqrt{7}\)
설명
Rationalizing \(\frac{2}{3 - \sqrt{7}}\) by multiplying through with \(3 + \sqrt{7}\),
\(\frac{2}{3 - \sqrt{7}} \frac{(3 + \sqrt{7})}{(3 + \sqrt{7})} = \frac{6 + 2\sqrt{7}}{9 - 7}\)
= \(\frac{6 + 2\sqrt{7}}{2} = 3 + \sqrt{7}\)