Question

If two positive numbers are in the ratio of $3+2\sqrt{2}:3-2\sqrt{2}$, then the ratio between their AM and GM is

• A. $6:1$
• B. $3:2$
• C. $2:1$
• D. $3:1$
• E. $1:6$

Answer 1

Answer: (D)

$3:1$

Let the two numbers be $a$ and $b$, then

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

$\Rightarrow a=(3+2\sqrt{2})k,b=(3-2\sqrt{2})k$

$\text{AM}=\frac{a+b}{2}=3k$

$\text{GM}=\sqrt{ab}=\sqrt{k^2}=k$

Therefore, $AM:AG=3k:k=3:1$