Math, asked by riya8190, 1 year ago

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

Answers

Answered by Yashikatuteja
4
hey....your answer....
Attachments:
Answered by shadowsabers03
4

 a = 2 + \sqrt{3} \\ \\ a^2 = (2 + \sqrt{3})^2 = 7 + 4\sqrt{3} \\ \\ a - \frac{1}{a} = \frac{a^2}{a} - \frac{1}{a} = \frac{a^2 - 1}{a} = \frac{7 + 4\sqrt{3} - 1}{2 + \sqrt{3}} = \frac{6 + 4\sqrt{3}}{2 + \sqrt{3}} \\ \\ = \frac{(6 + 4\sqrt{3})(2 - \sqrt{3})}{(2 + \sqrt{3})(2 - \sqrt{3})} = \frac{(6 + 4\sqrt{3})(2 - \sqrt{3})}{2^2 - (\sqrt{3})^2} = \frac{(6 + 4\sqrt{3})(2 - \sqrt{3})}{4 - 3} = \frac{(6 + 4\sqrt{3})(2 - \sqrt{3})}{1} \\ \\ = (6 + 4\sqrt{3})(2 - \sqrt{3}) = 12 - 6\sqrt{3} + 8\sqrt{3} - 12

 = 2\sqrt{3}


2√3 is the answer.


Hope this may be helpful.


Please mark my answer as the brainliest if this helps you.


Thank you. Have a nice day.

Similar questions