Question

find the value of A and B if under root 3 + 1 upon under root 3 minus 1 is equal to a + b under root 3

Answer 1

PLZ MARK MY ANSWER AS BRAINLIEST

Answer 2

Heya Friend,
Here is the answer you were looking for:

Identities used :

${(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab \\ (a + b)(a - b) = {a}^{2} - {b}^{2}$

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

On rationalizing the denominator we get,

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

Hope this helps!!!

Feel free to ask in the comment section if you have any doubt regarding to my answer...

@Mahak24

Thanks...
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