Question

Which option is right?​

Answer 1

Step-by-step explanation:

$\frac{ \sqrt{3} + 1 }{ \sqrt{3} - 1 } = \alpha + \beta \sqrt{3} \\ rationalising \: the \: denominator....... \\ \frac{ {( \sqrt{3} + 1) }^{2} }{2} \\ \frac{3 + 1 + 2 \sqrt{3} }{2} \\ \frac{4 + 2 \sqrt{3} }{2} \\ \frac{2 + (1) \sqrt{3} }{1} = \alpha + \beta \sqrt{3} \\ from \: here... \\ \alpha = 2 \: \: and \: \: \beta = 1$