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

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})