Simplify \(\frac{1}{(1-\sqrt{3})^{2}}\)
FURTHER MATHEMATICS
WAEC 2017
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. \(1+\sqrt{3}\)
Correct Answer: B. \(1+ \frac{1}{2}\sqrt{3}\)
Explanation
\(\frac{1}{(1-\sqrt{3})^{2}}\)
\((1-\sqrt{3})^{2} = (1-\sqrt{3})(1-\sqrt{3})\)
\(1 - 2\sqrt{3} + 3 = 4 - 2\sqrt{3}\)
\(\frac{1}{4-2\sqrt{3}}\)
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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