Simplify frac 1 sqrt 3 2 in the form a b sqrt 3 - JAMB Mathematics 2004 Question
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
correct option: a
\(\frac{1}{\sqrt{3}+2}=\frac{1}{\sqrt{3}+2}\times \frac{\sqrt{3}-2}{\sqrt{3}-2}\=\frac{\sqrt{3}-2}{(\sqrt{3})^{2} -2^{2}}\=\frac{\sqrt{3}-2}{3-4}=\frac{\sqrt{3}-2}{1}\=-\sqrt{3}+2\=2-\sqrt{3}\)
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