Question

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

Answer 1

a = 9/2 , b = 1/2

Hope it helps, please mark as brainliest

Answer 2

Solution;

Given,

$\frac{ \sqrt{11 - } \sqrt{7} }{ \sqrt{11} + \sqrt{7} } = a - b \sqrt{77}$

To find:

The values of a and b

Now rationalizing

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

On comparing with,

a-b√77

We derive that,

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

Verification:

Putting the values back,we obtain:

$\frac{9 - \sqrt{77} }{2}$