Question

find the rational number A and B such that root 2-1 upon root 2+1 =a+b root 2​

Answer 1

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

Hence,

$a = 3 \\ b = - 2$