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  • If a = 2 + sqroot 3 then find the value of a- 1 by a

If a = 2 + \sqrt{3} then find the value of a-\frac{1}{a}

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Answer.          2\sqrt{3}
Solution.   Given that a = 2\sqrt{3}

\therefore We have \frac{1}{a}= \frac{1}{2+\sqrt{3}}
Rationalising,
\Rightarrow \frac{1}{a}= \frac{1}{2+\sqrt{3}}\times \frac{2-\sqrt{3}}{2-\sqrt{3}}
Using   (a – b) (a + b) = a2 – b2

\Rightarrow \frac{1}{a}= \frac{2-\sqrt{3}}{2^{2}-\sqrt{3}^{2}}= \frac{2-\sqrt{3}}{4-3}
\Rightarrow \frac{1}{a}=2-\sqrt{3}
Now, a- \frac{1}{a}=2+\sqrt{3}-\left ( 2-\sqrt{3} \right )

\Rightarrow a- \frac{1}{a}=2\sqrt{3}

Hence the answer is 2\sqrt{3}

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infoexpert27

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