Question

square root 2 minus one by root 2 Plus 1 equals to a + b root 2

Answer 1

Hey friend,
Here is the answer you were looking for:
$\frac{ \sqrt{2} - 1}{ \sqrt{2} + 1 } = a + b \sqrt{2} \\ \\ on \: rationalizing \: the \: denominator \: we \: get \\ \\ = \frac{ \sqrt{2} - 1 }{ \sqrt{2} + 1} \times \frac{ \sqrt{2} - 1 }{ \sqrt{2} - 1 } \\ \\ = \frac{ {( \sqrt{2} )}^{2} + {(1)}^{2} - 2 \times \sqrt{2} \times 1}{ {( \sqrt{2}) }^{2} - {(1)}^{2} } \\ \\ = \frac{2 + 1 - 2 \sqrt{2} }{2 - 1} \\ \\ 3 - 2 \sqrt{2} = a + b \sqrt{2} \\ \\ a = 3 \\ \\ b = - 2$


Hope this helps!!!

@Mahak24

Thanks...
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