Question

√3 - 1 upon √3 + 1 = a + b √3

Answer 1

Hey user

Here is your answer :-

$\frac{ \sqrt{3} - 1}{ \sqrt{3} + 1 } = x + y \sqrt{3} \\ \\ \frac{( \sqrt{3} - 1)( \sqrt{3} + 1)}{( \sqrt{3} + 1)( \sqrt{3} - 1) } = x + y \sqrt{3} \\ \\ \frac{ {( \sqrt{3} - 1) }^{2} }{ { \sqrt{3} }^{2} - {1}^{2} } = x + y \sqrt{3} \\ \\ \frac{3 + 1 - 2 \sqrt{3} }{3 - 1 } = x + y \sqrt{3} \\ \\ \frac{4 - 2 \sqrt{ 3} }{2} = x + y \sqrt{3} \\ \\ 2 - 2 \sqrt{3} = x + y \sqrt{3} \\ \\ so \: x = 2 \: and \: y = - 1$

thank you.