Question

State True or False.

$\frac{\sqrt{11}-\sqrt{7}}{\sqrt{11}+\sqrt{7}}=\frac{9}{2}-\frac{1}{2}\sqrt{77}$

• A. True
• B. False

Answer 1

The correct option is A True

As given $\frac{\sqrt{11}-\sqrt{7}}{\sqrt{11}+\sqrt{7}}=a-\sqrt{77}b$
$=\frac{\sqrt{11}-\sqrt{7}}{\sqrt{11}+\sqrt{7}}\times \frac{\sqrt{11}-\sqrt{7}}{\sqrt{11}-\sqrt{7}}$
$=\frac{{(\sqrt{11}-\sqrt{7})}^2}{{\left(\sqrt{11}\right)}^2-{\left(\sqrt{7}\right)}^2}$
$=\frac{18-2\sqrt{77}}{4}$
Now comparing L.H.S with R.H.S
$\frac{18-2\sqrt{77}}{4}=a-\sqrt{77}b$
$18-2\sqrt{77}=4a-4\sqrt{77}b$
$a=\frac{18}{4}=\frac{9}{2}$
$b=\frac{-2\sqrt{77}}{-4\sqrt{77}}=\frac{1}{2}$