Question

√11+√7 by √11-√7 is equal to a- √77b

Answer 1

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