Question

Divide 36 in two parts such that sum of their reciprocals is 1/8

Answer 1

Answer:

24,12

Step-by-step explanation:

Let the two parts of 36 be x and y

so x+y=36......(1)

The sum of their reciprocal is 1/8

So

$\frac{1}{x} + \frac{1}{y} = \frac{1}{8}$

cross multiplying

$\frac{ x+ y}{xy} = \frac{1}{8}$

but x+y=36 , put this in above equation

$\frac{36}{xy} = \frac{1}{8}$

so xy= 288

Now put

$x = \frac{288}{y}$

in x+y=36

$\frac{288}{y} + y = 36$

multiply the whole equation by y and take the terms to one side

${y}^{2} - 36y + 288 = 0$

so we get the solution as

y=12, 24

so we put this y in x= 288/y

so x=24, 12

So the solution is

24,12

36 is divided into 12 and 24