Question

Find the value of a and b
√11-√7/√11+√7=a-b√77

Answer 1

Hey friend, Here is your answer-

$\frac{ \sqrt{11} - \sqrt{7} }{ \sqrt{11} + \sqrt{7} } = a - b \sqrt{77} \\ \frac{ \sqrt{11} - \sqrt{7} }{ \sqrt{11} + \sqrt{7} } \times \frac{ \sqrt{11} - \sqrt{7} }{ \sqrt{11} - \sqrt{7} } = a - b \sqrt{77} \\ \frac{18 - \sqrt{77} }{4} = a - b \sqrt{77} \\ \frac{9 - \sqrt{77} }{2}= a- b root 77 \\ a = 9 \: \: \: and \: \: \: b = 1$

I solved it by rationalisation of LHS.

Hope it will help you

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