Math, asked by ramsha517, 9 months ago

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

Answers

Answered by Aakrishisinha
4

Answer:

2√3 is the answer

Step-by-step explanation:

Mark this as BRAINLIEST

Attachments:
Answered by Blossomfairy
3

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} }

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

So,the answer is 23..

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