Question

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

Answer 1

HOPE THIS WILL HELP YOU

Answer 2

Answer:

$2 \sqrt{3}$

Step-by-step explanation:

$a = 2 + \sqrt{3} \\ \\ \frac{1}{a} = \frac{1}{2 + \sqrt{3} } \\ \\ = \frac{1 \times (2 - \sqrt{3} )}{(2 + \sqrt{3})(2 - \sqrt{3} ) } \\ \\ = \frac{2 - \sqrt{3} }{4 - 3} = 2 - \sqrt{3} \\ \\ a - \frac{1}{a} = 2 + \sqrt{3} - (2 - \sqrt{3} ) \\ \\ = 2 + \sqrt{3} - 2 + \sqrt{3} = 2 \sqrt{3}$

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