Question

Find the AM, GM and HM between $12$ and $30$

Answer 1

We know that the arithmetic mean between the two numbers $a$ and $b$ is $AM=\frac{a+b}{2}$, the geometric mean is $GM=\sqrt{ab}$ and the harmonic mean is $HM=\frac{2ab}{a+b}$.

Here, it is given that $a=12$ and $b=30$, therefore,

$AM=\frac{a+b}{2}=\frac{12+30}{2}=\frac{42}{2}=21$

$GM=\sqrt{ab}=\sqrt{12\times 30}=6\sqrt{10}$

$HM=\frac{2ab}{a+b}=\frac{2\times 12\times 30}{12+30}=\frac{720}{42}=\frac{120}{7}$

Hence, $AM=21$, $GM=6\sqrt{10}$ and $HM=\frac{120}{7}$