Question

if a=2+$\sqrt{3}$ find the 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,

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

Putting x = 2
and y = √3

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


Hope this helps!!!

@Mahak24

Thanks...
☺☺