Simplify (frac{1}{sqrt{3}+2}) in the form (a+bsqrt{3})
-
A.
2 -√3 -
B.
-2 – √3 -
C.
2 + √3 -
D.
-2 + √3
Correct Answer: Option A
Explanation
(frac{1}{sqrt{3}+2}=frac{1}{sqrt{3}+2}times frac{sqrt{3}-2}{sqrt{3}-2}\=frac{sqrt{3}-2}{(sqrt{3})^{2} -2^{2}}\=frac{sqrt{3}-2}{3-4}=frac{sqrt{3}-2}{1}\=-sqrt{3}+2\=2-sqrt{3})