Question

if 1,x,3 are in H.P., then find x

Answer 1

The complete solution for the above question is given as below:-

Since, 1, x, and 3 are in H.P. (It is given)

Then 1/1, 1/x and 1/3 are in A.P.

So, 1/x - 1/1 = 1/3 - 1/x

or 1/x + 1/x = 1 + 1/3

or 2/x = 4/3

or x/2 = 3/4

or x = 3/2

Answer 2

Answer:

The value of x= $\frac{3}{2}$

Step-by-step explanation:

Given,

1,x,3 are in H.P

To find,

The value of 'x'

Recall the concepts

Three numbers are said to be in Harmonic progression(H.P), if their reciprocal are in Arithmetic progression(A.P)

If three numbers a,b,c are in AP. Then, b-a = c-b

Solution:

Given that the three numbers 1,x,3 are in H.P

Then by definition, we $\frac{1}{1} ,\frac{1}{x} ,\frac{1}{3}$ are in AP

Since  $\frac{1}{1} ,\frac{1}{x} ,\frac{1}{3}$ are in AP, we have

$\frac{1}{x} -\frac{1}{1} =\frac{1}{3} - \frac{1}{x}$

$\frac{1}{x} +\frac{1}{x} = \frac{1}{3}+1$

$\frac{2}{x} = \frac{4}{3}$

4x = 6

x = $\frac{6}{4}$ = $\frac{3}{2}$

∴ The value of x= $\frac{3}{2}$

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