Question
If the ratio of the arithmetic mean and the geometric mean of two positive numbers is $3: 2$, then find the ratio of the geometric mean and the harmonic mean of the numbers.(1) $2: 3$(2) $9: 4$(3) $3: 2$(4) $4: 9$
Step 1
The arithmetic mean (AM) of these numbers is $\frac{a+b}{2}$ and the geometric mean (GM) is $\sqrt{ab}$. We are given that the ratio of AM to GM is $3:2$. So, we can write this as: \[\frac{\frac{a+b}{2}}{\sqrt{ab}} = \frac{3}{2}\] Show more…
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