Question

Find the values of $a$ and $b$ if
$\frac{3+\sqrt{2}}{3-\sqrt{2}}=a+b\sqrt{2}$

Answer 1

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

$\frac{11+6\sqrt{2}}{7}=a+b\sqrt{2}$

$a=\frac{11}{7},b=\frac{6}{7}$