Question

Find the value of $a$ and $b$ in $\frac{3+\sqrt{7}}{3-\sqrt{7}}=a+b\sqrt{7}$

• A. $a=8,b=3$
• B. $a=3,b=8$
• C. $a=8,b=5$
• D. None of these

Answer 1

Answer: (A)

$a=8,b=3$

$\frac{3+\sqrt{7}}{3-\sqrt{7}}\times \frac{(3+\sqrt{7})}{(3-\sqrt{7})}=a+b\sqrt{7}$

$\therefore \frac{(3+\sqrt{7}{)}^2}{3^2-(\sqrt{7}{)}^2}$=$a+b\sqrt{7}=\frac{9+7+6\sqrt{7}}{9-7}=a+b\sqrt{7}$

$\frac{16+6\sqrt{7}}{2}=a+b\sqrt{7}$

$8+3\sqrt{7}=a+b\sqrt{7}$

on comparing $a=8$ and $b=3$