Question

√2+1∕√2-1 – √2-1/√2+1 = a+√2b then find a and b

Answer 1

Answer:

$\frac{ \sqrt{2} + 1 }{ \sqrt{2} - 1} - \frac{ \sqrt{2} - 1 }{ \sqrt{2} + 1 } = a + \sqrt{2}b \\ \frac{ {( \sqrt{2} + 1) }^{2} - ( { \sqrt{2} - 1)}^{2} }{ { \sqrt{2} }^{2} - {1}^{2} } \\ \frac{2 + 1 + 2 \sqrt{2} - (2 + 1 - 2 \sqrt{2)} }{2 - 1} \\ \frac{3 + 2 \sqrt{2} - (3 - 2 \sqrt{2} )}{1} \\ 3 + 2 \sqrt{2} - 3 + 2 \sqrt{2} = 0 + 4 \sqrt{2} \\ a \: = 0 \\ b \: = 4$