Question

If a = 2+ √3 , then find the value of a - 1/a​

Answer 1

ANSWER :-

$a = 2 + \sqrt{3}$

$then \\ \frac{1}{a} = \frac{1}{2 + \sqrt{3} } \\ by \: rationalising \: we \: get \\ \frac{1}{a} = \frac{2 - \sqrt{3} }{4 - 3} = 2 - \sqrt{3}$

$therefore \\ a - \frac{1}{a} = 2 + \sqrt{3} - 2 + \sqrt{3} \\ \implies a - \frac{1}{a} = 2 \sqrt{3}$

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