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JAMB 2017 · UTME (set 2) · Q33

If 23−23+22=m+n6\dfrac{2\sqrt3 - \sqrt2}{\sqrt3 + 2\sqrt2} = m + n\sqrt6, find the values of mm and nn respectively.

Worked solution (try it first)
  1. Multiply the top and bottom by the conjugate of the bottom, 3−22\sqrt3 - 2\sqrt2.
  2. Bottom: (3+22)(3−22)=3−8(\sqrt3 + 2\sqrt2)(\sqrt3 - 2\sqrt2) = 3 - 8, which is −5-5.
  3. Top: (23−2)(3−22)=6−46−6+4(2\sqrt3 - \sqrt2)(\sqrt3 - 2\sqrt2) = 6 - 4\sqrt6 - \sqrt6 + 4, which is 10−5610 - 5\sqrt6.
  4. Divide by −5-5: −2+6-2 + \sqrt6.
  5. So m=−2m = -2 and n=1n = 1, option B.

Also set as JAMB 2000 · UME · Q3

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