Question

if a=2+√3 , then find value of a-1/a with method
Plz do I will mark as brainleist​

Answer 1

Answer:

★ a = 2 + √3

★ 1/a = 1/(2 + √3)

= 1/(2 + √3) x (2 - √3)/(2 - √3)

= (2 - √3) / [(2)² - (√3)²]

= (2 - √3) / 4 - 3

= 2 - √3

A.T.Q

➟ a - 1/a

➟ 2 + √3 - ( 2 - √3 )

➟ 2 + √3 - 2 + √3

➟ 2√3

Answer 2

SOLUTION

Given,

a= 2+√3

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

Now,

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

hope it helps ☺️