Question

Find the AM, GM and HM between $-8$ and $-42$

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 $a=-8$ and $b=-42$, therefore,

$AM=\frac{a+b}{2}=\frac{-8+(-42)}{2}=\frac{-8-42}{2}=\frac{-50}{2}=-25$

$GM=\sqrt{ab}=\sqrt{(-8)\times (-42)}=\sqrt{336}=4\sqrt{21}$

$HM=\frac{2ab}{a+b}=\frac{2\times (-8)\times (-42)}{-8+(-42)}=\frac{672}{-8-42}=-\frac{336}{25}$

Hence, $AM=-25$, $GM=4\sqrt{21}$ and $HM=-\frac{336}{25}$