Question

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

Answer 1

$\huge\underline \frak \red{Answer}$

$given \: a = 2 + \sqrt{3 } \\ then \ \: \frac{1}{a} = \frac{1}{2 + \sqrt{3} } \\ \implies \: to \: find \: a - \frac{1}{a} \\ \implies \: 2 + \sqrt{3} - \frac{1}{2 + \sqrt{3} } \\ by \: doing \: lcm \: \\ \frac{ (2 + \sqrt{3} )(2 + \sqrt{3} ) - 1}{2 + \sqrt{3} } \\ \implies \: \frac{4 + 2 \sqrt{3} + 2 \sqrt{3} + 3 - 1 }{2 + \sqrt{3} } \\ \implies \: \frac{4 \sqrt{3} + 6}{2 + \sqrt{3} }$

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