Question

root over 2-1/root over 2+1=a+broot over2​

Answer 1

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

Therefore when we compare the two sides ie, LHS and RHS we get that

x = √3/3 and

y = 0

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