Question

The two harmonic means between 5 and 10

Answer 1

 2 / 1/5 + 1/10
= 2/0.2+0.1
= 2/0.3
= 2/3/10
= 2 *10/3
= 20/3

Answer 2

Answer:

Therefore,  $H_{1} = 6$ and $H_{2} = \frac{15}{2}$ the two harmonic means between 5 and 10.

Step-by-step explanation:

Insert two HM  between 5 and  10

Let , a = 5  and  b = 10

And  $H_{1}$ and $H_{2}$ be the two  HM

$\frac{1}{5}, \frac{1}{H_{1} } ,\frac{1}{H_{2} }, \frac{1}{10}$ are in AP , where d is the common difference of this in AP

∴$\frac{1}{10}= (n+2)^{th}$term = $T_{n+2}$

$\frac{1}{10} = \frac{1}{5} + ((n + 2 )- 1)d\\d = \frac{\frac{1}{10}-\frac{1}{5} }{n+1}$

For n = 2, (already given)

$d=\frac{\frac{1}{10}-\frac{1}{5} }{3} = \frac{1-2}{10 X 3 } = \frac{-1}{30}$

$T_{2} = \frac{1}{5}$$+ (2-1)$×$\frac{-1}{30}$ = $\frac{6-1}{30} = \frac{5}{30} = \frac{1}{6}$ = $\frac{1}{H_{1} }$

$T_{3} = \frac{1}{5} + (2$×$\frac{-1}{30})$ $\frac{3-1}{15} = \frac{2}{15}$ = $\frac{1}{H_{2} }$

Therefore,  $H_{1} = 6$ and $H_{2} = \frac{15}{2}$ the two harmonic means between 5 and 10.

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