Question

find a and b if
1 - root 3 / 1 + root 3 = a + root b

Answer 1

Please mark it as a brainlist

Answer 2

Hey there !!
Here's your answer

Given,
to find a and b in

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

Rationalizing the denominator,
we have,

$\frac{(1 - \sqrt{3})(1 - \sqrt{3} ) }{(1 + \sqrt{3})(1 - \sqrt{3}) } = a + \sqrt{b}$
Using the identity (a - b)(a + b) = a² - b² in the denominator and (a-b)(a-b)=a²- 2ab + b²



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


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


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

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


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

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

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

comparing on both the sides,
we have,

a = -2
b = 3