Question

√11-√7/√11+√7=a-b√77

Answer 1

I think it will help u

Answer 2

$Given \:\frac{( \sqrt{11} - \sqrt{7})}{( \sqrt{11} + \sqrt{7})} = a - b\sqrt{77}$

$LHS = \frac{( \sqrt{11} - \sqrt{7})}{( \sqrt{11} + \sqrt{7})}$

$= \frac{( \sqrt{11} - \sqrt{7})(\sqrt{11} - \sqrt{7})}{( \sqrt{11} + \sqrt{7})(\sqrt{11} - \sqrt{7})}$

$= \frac{( \sqrt{11} - \sqrt{7})^{2}}{( \sqrt{11})^{2} - (\sqrt{7})^{2}} \\= \frac{ \sqrt{11}^{2} + \sqrt{7}^{2} - 2\times \sqrt{11} \times \sqrt{7} }{11 - 7} \\= \frac{11 + 7 - 2\sqrt{77} }{ 4 } \\= \frac{18- 2\sqrt{77} }{ 4 } \\= \frac{2(9- \sqrt{77}) }{ 4 } \\= \frac{9- \sqrt{77} }{ 2 } \\= \frac{9}{2} - \frac{1}{2}(\sqrt{77}) \: --(1)$

$Now, \pink{Compare \: \frac{9}{2} - \frac{1}{2}(\sqrt{77}) = a - b \sqrt{77}}$

$a = \frac{9}{2} \: and \: b = \frac{1}{2}$

Therefore.,

$\green { a = \frac{9}{2} \: and \: b = \frac{1}{2} }$

•••♪