Question

√11-√7÷√11-√7=a-b√77

Answer 1

a=sqrt(l l)-sqrt(7) ; b=l÷ll

Answer 2

Answer:

⇒ a = 9/2 and b = 1/2

Step-by-step explanation:

We have ,

$= > \frac{ \sqrt{11} - \sqrt{7} }{ \sqrt{11} + \sqrt{7} }$

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

$= > \frac{( \sqrt{11} - \sqrt{7}) ^{2}}{( \sqrt{11})^{2} - ( \sqrt{7}) ^{2} }$

$= > \frac{11 + 7 - 2 \times \sqrt{11} \times \sqrt{7} }{11 - 7}$

$= > \frac{(18 - 2 \sqrt{77} )}{4}$

$= > ( \frac{18}{4} - \frac{2}{4} \sqrt{77})$

$= > ( \frac{9}{4} - \frac{1}{2} \sqrt{77})$

∴ √11 - √7 / √11 + √7 = a - b√77

Comparing on both sides , we get ;

$= > \frac{9}{2} - \frac{1}{2} \sqrt{77} = a - b \sqrt{77}$

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