Question

if a=2+√3, then find value of a-1/a

Answer 1

Heya friend,
Here is the answer you were looking for:
$a = 2 + \sqrt{3} \\ \\ \frac{1}{a} = \frac{1}{2 + \sqrt{3} }$

On rationalizing the denominator we get,

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

Using the identity :

$(x + y)(x - y) = {x}^{2} - {y}^{2}$

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

Putting the values,

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

Hope this helps!!!

Feel free to ask in the comment section if you have any doubt regarding to my answer...

@Mahak24

Thanks...
☺☺

Answer 2

Answer:

a - $\frac{1}{a}$  =2√3

Step-by-step explanation:

Given,

a = 2+√3

To find,

a - $\frac{1}{a}$

Solution:

a = 2+√3

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

The rationalizing factor is 2 - $\sqrt{3}$

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

= $\frac{2-\sqrt{3}}{4-3}$

=  2 - √3

a - $\frac{1}{a}$  = 2+√3 - (2-√3)

= 2+√3 - 2+√3

=2√3

∴a - $\frac{1}{a}$  =2√3

#SPJ2