Question

State True or False.

$\frac{3+\sqrt{7}}{3-\sqrt{7}}=8+3\sqrt{7}$

• A. True
• B. False

Answer 1

The correct option is A True

$\frac{3+\sqrt{7}}{3-\sqrt{7}}=a+b\sqrt{7}$
$\Rightarrow \frac{3+\sqrt{7}}{3-\sqrt{7}}\times \frac{3+\sqrt{7}}{3+\sqrt{7}}=a+b\sqrt{7}$
$\Rightarrow \frac{{(3+\sqrt{7})}^2}{(3^2-{\sqrt{7}}^2)}=a+b\sqrt{7}$
$\Rightarrow \frac{16+6\sqrt{7}}{2}=a+b\sqrt{7}$
$\Rightarrow 8+3\sqrt{7}=a+b\sqrt{7}$
Comparing LHS and RHS we get
$\Rightarrow a=8,b=3$