Simplify \(\frac{1}{\sqrt{3}+2}\) in the form \(a+b\sqrt{3}\)
A
2 -√3
B
-2 - √3
C
2 + √3
D
-2 + √3
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
\(\frac{1}{\sqrt{3}+2}\)
= \(\frac{1}{\sqrt{3}+2}\times \frac{\sqrt{3} - 2}{\sqrt{3} - 2}\)
= \(\frac{\sqrt{3}-2}{(\sqrt{3})^{2} -2^{2}}\)
= \(\frac{\sqrt{3}-2}{3-4}\)
= \(\frac{\sqrt{3}-2}{1}\) = -\(\sqrt{3}+2\)
= 2- \(\sqrt{3}\)
Source: Myschool Past Questions Archive (Record #8214)