Question

1+root3/1-root3=a-broot3

Answer 1

Answer:

Given:

$\dfrac{1+\sqrt{3}}{1-\sqrt{3}}=a-b\sqrt{3}$

To find : and 'a' and 'b'

Solving Question:

        we are given the fraction,so first we should simplify it for that we have  to rationalise the denominator .

Solution:

   $\dfrac{1+\sqrt{3}}{1-\sqrt{3}}* \dfrac{1+\sqrt{3}}{1+\sqrt{3}}=\dfrac{(1+\sqrt{3})^2}{1^2-(\sqrt{3})^2}\\\\\implies \dfrac{1+2\sqrt{3}+3}{-2}\\\\\implies \dfrac{4+2\sqrt{3}}{-2}\\\\\implies -2-\sqrt{3}$

Thus, ⇒ -2 -√3 = a - b√3

⇒ On comparing , we get

a = -2

b = 1

Thus,the value of 'a' is -2 and that of 'b' is 1