Question

If m = $\frac{1}{3-2\sqrt{2}}$ and $n=\frac{1}{3+2\sqrt{2}}$

then mn = _______.

• A. 81
• B. 27
• C. 9
• D. 1

Answer 1

The correct option is D

1

m = $\frac{1}{3-2\sqrt{2}}\times \frac{3+2\sqrt{2}}{3+2\sqrt{2}}$

=$\frac{3+2\sqrt{2}}{(3{)}^2-(2\sqrt{2}{)}^2}$

=$\frac{3+2\sqrt{2}}{9-8}$

=$3+2\sqrt{2}$ ...(i)

n =$\frac{1}{3+2\sqrt{2}}\times \frac{3-2\sqrt{2}}{3-2\sqrt{2}}$

=$\frac{3-2\sqrt{2}}{9-8}$

= $3-2\sqrt{2}$ ...(ii)

$mn=(3+2\sqrt{2})(3-2\sqrt{2})$ (from (i) and (ii) )

=$(3{)}^2-(2\sqrt{2}{)}^2$

=$9-8$

=$1$