Question

if (√3-1 ) divided by √3 +1 =a+b√3

find the value of a and b

Answer 1

a=2

b=-1

Hope it helps

Answer 2

Given : (√3 - 1)/(√3 + 1) = a + b√3.

On rationalizing, we get

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

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

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

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

$= > \frac{4 - 2\sqrt{3}}{2} = a + b\sqrt{3}$

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

⇒ 2 - √3 = a + b√3

⇒ 2 + (-1)√3 = a + b√3.

Therefore, the value of a = 2, b = -1.

Hope this helps!