Question

root11-1÷root11+1=a-b root11​

Answer 1

Solution:-

$\frac{\sqrt{11} - 1}{ \sqrt{11} + 1} = a - b \sqrt{11} \\ \\ \frac{\sqrt{11} - 1}{ \sqrt{11} + 1} \times \frac{\sqrt{11} - 1}{ \sqrt{11} - 1} = a - b \sqrt{11} \\ \\ \frac{{ \:(\sqrt{11} - 1) }^{2} }{ { (\sqrt{11}) }^{2} - {1}^{2} } = a - b \sqrt{11} \\ \\ \frac{ \: { (\sqrt{11} )}^{2} + {(1)}^{2} - 2 \times \sqrt{11} \times 1 \: }{11 - 1} = a - b \sqrt{11} \\ \\ \frac{11 + 1 - 2 \sqrt{11} }{10} = a - b \sqrt{11} \\ \\ \frac{12 - 2 \sqrt{11} }{10} = a - b \sqrt{11} \\ \\ \frac{6 - \sqrt{11} }{5} = a - b \sqrt{11} \\ \\ \frac{6}{5} - \frac{1}{5} \sqrt{11} = a - b \sqrt{11} \\ compare \: both \: side \\ \\ a = \frac{6}{5} \: \: and \: \: b = \frac{1}{5}$

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