Question

kindly tell accurate answer for this question ! and if u will scribble I will surely report your account !​

Answer 1

$\Huge{\textbf{\textsf{{\purple{Ans}}{\pink{wer}}{\color{pink}{:}}}}}$

$\frac{ \sqrt{3} - 1}{ \sqrt{3} + 1} \\ = \frac{( \sqrt{3} - 1)( \sqrt{3} - 1) }{( \sqrt{3} + 1)( \sqrt{3} - 1) } \\ = \frac{ {( \sqrt{3} - 1)}^{2} }{ {( \sqrt{3} )}^{2} - {1}^{2} } \\ = \frac{ {( \sqrt{3} )}^{2} - 2 \sqrt{3} + {1}^{2} }{3 - 1} \\ = \frac{3 - 2 \sqrt{3} + 1 }{2} \\ = \frac{2 + 2 \sqrt{3} }{2} \\ = \frac{2(1 + \sqrt{3} )}{2} \\ = \frac{ \cancel 2 \: (1 + \sqrt{3} )}{ \cancel 2} \\ = 1 + \sqrt{3} \\ \implies \: 1 + \sqrt{3} = a + b \sqrt{3} \: \: \: \: [given] \\ \therefore \: a = 1 \\ \: \: \: \: \: b = 1$