Question

$\frac{1}{\left(3+2\sqrt{2}\right)}=?$

(a) $\frac{{\displaystyle 3-2\sqrt{2}}}{{\displaystyle 17}}$

(b) $\frac{\left(3-2\sqrt{2}\right)}{13}$

(c) $\left(3-2\sqrt{2}\right)$

(d) None of these

Answer 1

$\frac{1}{\left(3+2\sqrt{2}\right)}=\frac{1}{\left(3+2\sqrt{2}\right)}\times \frac{\left(3-2\sqrt{2}\right)}{\left(3-2\sqrt{2}\right)}=\frac{\left(3-2\sqrt{2}\right)}{9-8}=\left(3-2\sqrt{2}\right)$
Hence, the correct answer is option (c).