Question

If a and b are rational numbers and √11-√ 7)/√11 +√ 7=a -b √77.Find the value of a and b​

Answer 1

Answer:

........................

Answer 2

Answer:

Step-by-step explanation:

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

$\frac{\sqrt{11}-\sqrt{7} }{\sqrt{11}+\sqrt{7} }$  × $\frac{\sqrt{11}-\sqrt{7} }{\sqrt{11} -\sqrt{7} }$

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

$\frac{(11+7-2.\sqrt{11} .\sqrt{7} }{11-7}$

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

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

comparing with $a-b\sqrt{77}$

hence,

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