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JAMB 2011 · UTME · Q8

Rationalize 2−53−5\dfrac{2 - \sqrt5}{3 - \sqrt5}.

Worked solution (try it first)
  1. Multiply the top and bottom by the conjugate of the bottom, 3+53 + \sqrt5.
  2. Bottom: (3−5)(3+5)=9−5(3 - \sqrt5)(3 + \sqrt5) = 9 - 5, which is 4.
  3. Top: (2−5)(3+5)=6+25−35−5(2 - \sqrt5)(3 + \sqrt5) = 6 + 2\sqrt5 - 3\sqrt5 - 5, which is 1−51 - \sqrt5.
  4. So the value is 1−54\dfrac{1 - \sqrt5}{4}, option B.

Also set as JAMB 2017 · UTME · Q27

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