Question

if a=2+√3,then find the value of a -1/a
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Answer 1

Answer:

2√3 is the answer

Step-by-step explanation:

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Answer 2

Given :

• a = 2 + √3

To find :

• The value of a - 1/a

According to the question,

Rationalising 1/a we get,

$\implies \bf{ \dfrac{1}{a} = \dfrac{1}{2 + \sqrt{3} } \times \dfrac{2 - \sqrt{3} }{2 - \sqrt{3} } }$

$\implies \bf{ \dfrac{1}{a} = \dfrac{2 - \sqrt{3} }{4 - 3} = 2 - \sqrt{3} \: \pink\bigstar}$

Now solving a - 1/a we get,

$\therefore \bf{a - \dfrac{1}{a} = 2 + \sqrt{3} - \big(2 - \sqrt{3} \big) }$

$\implies \bf{2 + \sqrt{3} - 2 +\sqrt{3} }$

${ \underline{\boxed{\implies{ \bf{2 \sqrt{3} }}}}} \: \red \bigstar$

So,the answer is 2√3..

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