Question

√2-1/√2+1=a+b√2. find rational numbers a and b

Answer 1

Hello Mate!

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

Hope it helps☺!
Ping me out for any confusions.

Answer 2

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