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in Number System by (36.7k points)
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If x = 2 + √3 , then the value of x – 1/x is 

A) 4 

B) √3

C) 2√3 . 

D) 2 +√3

2 Answers

+1 vote
by (57.0k points)
selected by
 
Best answer

Correct option is (C) 2√3

\(\because\) \(x=2+\sqrt{3}\)

\(\therefore\) \(\frac1x=\frac1{2+\sqrt{3}}\) \(=\frac1{2+\sqrt{3}}\times\frac{2-\sqrt{3}}{2-\sqrt{3}}\)

\(=\frac{2-\sqrt{3}}{4-3}\) \(=2-\sqrt{3}\)

\(\therefore\) \(x-\frac1x=2+\sqrt{3}-(2-\sqrt{3})=2\sqrt{3}\)

+1 vote
by (38.9k points)

Correct option is  B) √3

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