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: Option B
Explanation
(frac{1}{(1-sqrt{3})^{2}})
((1-sqrt{3})^{2} = (1-sqrt{3})(1-sqrt{3}))
(1 – 2sqrt{3} + 3 = 4 – 2sqrt{3})
(frac{1}{4-2sqrt{3}})
After rationalising (multiplying the denominator and numerator with (4+2sqrt{3}), we have
(frac{4+2sqrt{3}}{4} = 1 + frac{1}{2}sqrt{3})