Question on: JAMB Mathematics - 2024
Rationalize \(\frac{2 - \sqrt5}{3 - \sqrt5}\)
A
\(\frac{1 - \sqrt5}{2}\)
B
\(\frac{1 - \sqrt5}{4}\)
C
\(\frac{\sqrt5 - 1}{2}\)
D
\(\frac{1 + \sqrt5}{4}\)
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Correct Option: B
Multiply numerator and denominator by the conjugate:
\[ \frac{2 - \sqrt5}{3 - \sqrt5} \times \frac{3 + \sqrt5}{3 + \sqrt5} \]
Expand:
\[ (2 - \sqrt5)(3 + \sqrt5) = 6 + 2\sqrt5 - 3\sqrt5 - 5 = 1 - \sqrt5 \]
\[ (3 - \sqrt5)(3 + \sqrt5) = 9 - 5 = 4 \]
Thus:
\[ \frac{1 - \sqrt5}{4} \]
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