Simplify \;{1}{(1-{3})²}

Correct Answer is : 1+ 1231+ \;1/2{3}1+213

Correct Answer is : 1+ 1231+ \;1/2{3}1+213

Test Index

WAEC Further Mathematics 2017 Paper

Question : 3

Total: 40

Simplify

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

Solution:

Concept:

Simplify by expanding the perfect square, then rationalise the denominator.

Explanation:

First, expand the square in the denominator.

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

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

So the given expression becomes

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

To rationalise, multiply the numerator and denominator by the conjugate

4 + 2\sqrt{3}

\frac{1}{4 - 2\sqrt{3}} \times \frac{4 + 2\sqrt{3}}{4 + 2\sqrt{3}}

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

= \frac{4 + 2\sqrt{3}}{16 - 12} = \frac{4 + 2\sqrt{3}}{4}

= 1 + \frac{\sqrt{3}}{2} = 1 + \frac{1}{2}\sqrt{3}

This matches option B.

Answer:

1 + \frac{1}{2}\sqrt{3}

(Option B).

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