Simplify ( \(\frac{1}{2 - √3}\) + \(\frac{2}{2 + √3}\) )\(^{-1}\)

  • A \(\frac{-1}{33}\)(6 + √3)
  • B \(\frac{-1}{33}\)(6 - √3)
  • C \(\frac{1}{33}\)(6 + √3)
  • D \(\frac{1}{33}\)(6 - √3)
waec 2021furthermathematics

The correct answer is C. \(\frac{1}{33}\)(6 + √3)

( \(\frac{1}{2 - âˆš3}\) + \(\frac{2}{2 + âˆš3}\) )\(^{-1}\)

= \(\frac{2 + âˆš3 + 2(2 - âˆš3)}{(2 - âˆš3)(2 + âˆš3)}\)

= 2 + âˆš3 + 4 - 2√3 

= (6 - âˆš3)\(^{-1}\)

= \(\frac{1}{6 - âˆš3}\)

= \(\frac{6 + âˆš3}{6 - âˆš3  *  6 + âˆš3}\)

= \(\frac{6 + √3}{33}\)

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