Question

If a and b are rational numbers ,
$\frac{2 + \sqrt{3} }{2 - \sqrt{3 } } = a + b \sqrt{3}$
then, b is .......
The options are as follows:
a.4
b.7
c.6
d.8

please give me step by step method.
It's a request to not to give wrong answers.
I will be very much thankful for the answer.
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Answer 1

Answer:

Rationalise the denominator

(2+v3) ^2

..................

(2-v3) (2+v3)

=4+3+4v3

....................

4-3

=7+4v3

=a+bv3

a=7,b=4

Answer 2

Answer:

$\frac{2 + \sqrt{3} }{2 - \sqrt{3} }$

$multiplying \: by \: \frac{(2 + \sqrt{3}) }{(2 + \sqrt{3} )}$

$\frac{4 + 3 + 4 \sqrt{3} }{4 - 3}$

$\frac{7 + 4 \sqrt{3} }{1}$

$on \: comparing \: we \: get,$

$a = 7$

$b = 4$

Hope it Helps

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