Question

If $\frac{3+2\sqrt{2}}{3-\sqrt{2}}=a+b\sqrt{2}$ , then find the values of $a$ and $b$.

Answer 1

$\frac{3+2\sqrt{2}}{3-\sqrt{2}}=a+b\sqrt{2}$

$\Rightarrow \frac{3+2\sqrt{2}}{3-\sqrt{2}}\times \frac{3+\sqrt{2}}{3+\sqrt{2}}=a+b\sqrt{2}$

$\Rightarrow \frac{9+3\sqrt{2}+6\sqrt{2}+4}{9-2}=a-b\sqrt{2}$

$\Rightarrow \frac{13}{7}+\frac{9\sqrt{2}}{7}=a+b\sqrt{2}$

On comparing both the sides of

$a=\frac{13}{7}$ and $b=\frac{9}{7}$