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

  • A \(1- \frac{1}{2}\sqrt{3}\)
  • B \(1+ \frac{1}{2}\sqrt{3}\)
  • C \(\sqrt{3}\)
  • D \(1+\sqrt{3}\)
waec 2017furthermathematics

The correct answer is B. \(1+ \frac{1}{2}\sqrt{3}\)

\(\frac{1}{(1-\sqrt{3})^{2}}\) 

\((1-\sqrt{3})^{2} = (1-\sqrt{3})(1-\sqrt{3})\)

\(1 - 2\sqrt{3} + 3 = 4 - 2\sqrt{3}\)

\(\frac{1}{4-2\sqrt{3}}\)

After rationalising (multiplying the denominator and numerator with \(4+2\sqrt{3}\), we have

\(\frac{4+2\sqrt{3}}{4} = 1 + \frac{1}{2}\sqrt{3}\)

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