Question

root11-1÷root11+1=a-b root11​

Answer 1

$:\implies \frac{ \sqrt{11} - 1}{ \sqrt{11} + 1 } = a - b \sqrt{11} \\ \\ \:\implies \ \frac{ \sqrt{11} - 1}{ \sqrt{11} + 1 } \times \frac{ \sqrt{11} - 1}{ \sqrt{11} - 1 } = a - b \sqrt{11} \\ \\ :\implies \frac{ (\sqrt{11} - 1)( \sqrt{11} - 1) }{ (\sqrt{11} + 1)( \sqrt{11} - 1) } = a - b \sqrt{11} \\ \\ :\implies {( \sqrt{11}) }^{2} - 2( \sqrt{11} )(1) + {1}^{2} = a - b \sqrt{11}\\ \\:\implies 11 - 2 \sqrt{11} + 1 = a - b \sqrt{11} \\ \\ :\implies 12 - 2 \sqrt{11} = a - b \sqrt{11} \\ \\ :\implies \color{red} \boxed{ a= 12} \\ \\:\implies \color{red} \boxed{ b = 2}$

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