Question

find the values of a and b in√3+1/√3-1 = a+b√3​

Answer 1

Step-by-step explanation:

it's answer of your question

Answer 2

Step-by-step explanation:

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

TO FIND

Value of a and b

SOLUTION

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