Question

two harmonic means between 1/2 ,4/17 are​

Answer 1

Since 1/2,4/17 is in H.P.

Then 2 and 17/4 are in A.P

Now,let x and y be the two arithmetic means between 2&17/4.

Then,2 is the first term and 17/4 is the fourth term.

If d is the common difference,we have

17/4=2+(4-1)d

or 17=4(2+3d)

or 17=8+12d

or 12d=9

or d=3/4

Now two arithmetic means between 2&17/4 are 2+3/4 and 2+3/4+3/4 i.e. 11/4 and 14/4=7/2

Therefore two harmonic means between 1/2 and 4/17 are 4/11 and 2/7.

Thanks for giving me the chance to solve this question.

Hope this will help you.

Answer 2

Answer:

4/11 and 2/7.

Step-by-step explanation:

Let $x_1$ and $x_2$ be two H.M's between $\frac{1}{2} \,,\;\frac{4}{7}$.

∴ a = $\frac{1}{2}$ , b = $\frac{4}{17}$ , n = 2.

$x_1\;=\;\frac{ab(2+1)}{b(2+1)+1(a-b)}\;=\;\frac{3ab}{a+2b}$

$x_1\;=\;3(\frac{(1/2)(4/17)}{(1/2)+2(4/17)}\;=\;\frac{4}{11}$

$x_2\;=\;\frac{ab(2+1)}{b(2+1)+2(a-b)}\;=\;\frac{3ab}{2a+b}$

$x_2\;=\;3(\frac{(1/2)(4/17)}{2(1/2)+(4/17)}\;=\;\frac{2}{7}$

∴ $x_1$ and $x_2$ (The two H.M's) are 4/11 and 2/7.