Question

If $x=3-2\sqrt{2}$ , then $\frac{1}{x}=$ _____.

• A. $3+2\sqrt{2}$
• B. $3-2\sqrt{2}$
• C. $6\sqrt{2}$
• D. $6+2\sqrt{2}$

Answer 1

The correct option is A

$3+2\sqrt{2}$

$\frac{1}{x}$ = $\frac{1}{3-2\sqrt{2}}$

Rationalizing factor of the denominator is $3+\sqrt{2}$.

Multiplying both numerator and denominator by $3+\sqrt{2}$ , we get
= $\frac{1}{3-2\sqrt{2}}$ $\times$ $\frac{3+\sqrt{2}}{3+\sqrt{2}}$
= $\frac{3+2\sqrt{2}}{3^2-(2\sqrt{2}{)}^2}$
= $\frac{3+2\sqrt{2}}{9-8}$
= $3+2\sqrt{2}$

Hence $\frac{1}{x}$ = $3+2\sqrt{2}$