Question

if a=2+root 3 , find the value of a-1/a​

Answer 1

Answer:

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Answer 2

Answer:

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Step-by-step explanation:

Given,

$a = 2 + \sqrt{3}$

Therefore,

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

So,

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