Question

if √11-1/√11-1= a-b√11 then find the value of a and b​

Answer 1

Solution :

LHS :

> [√11 - 1 ]/[ √11 + 1]

> [√11 - 1 ]/[ √11 + 1] × [ √11 - 1]/[ √11 - 1]

> [√11 - 1]²/( 10 )

> [ 11 + 1 - 2√11 ]/10

> [ 12 - 2√11 ]/10

> 6/5 - √11/5

Hence

a = 6/5

b = 1/5 .

This is the required answer .

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Answer 2

Answer

$given \: \\ \\ \frac{ \sqrt{11} - 1 }{ \sqrt{11} + 1 } = a - b \sqrt{11} \\ \\ multiply \: nr \: and \: dr \: by \: \: \sqrt{11} - 1 \\ \\ \frac{ \sqrt{11} - 1}{ \sqrt{11} + 1 } \times \frac{ \sqrt{11} - 1 }{ \sqrt{11} - 1 } = a - b \sqrt{11} \\ \\ \frac{ (\sqrt{11} - 1) {}^{2} }{ (\sqrt{11}) {}^{2} - 1 {}^{2} } = a - b \sqrt{11} \\ \\ \frac{12 - 2 \sqrt{11} }{10} = a - b \sqrt{11} \\ \\ \frac{6 - \sqrt{11} }{5} = a - b \sqrt{11} \\ \\ \frac{6}{5} - \frac{ \sqrt{11} }{5} = a - b \sqrt{11} \\ \\ now \: compare \: coffecient \: \: of \: a \: and \: b \\ \\ a = \frac{6}{5} \: \: and \: \: b = \frac{1}{5}$