Question

divide 25 into two parts so that the sum of their reciprocals is 1/6

Answer 1

Let one part be x. Then, other part is 25-x
Given,
$\frac{1}{x} + \frac{1}{25 - x} = \frac{1}{6} \\ \frac{(25 - x) + x}{x(25 - x)} = \frac{1}{6} \\ \frac{25 }{x(25 - x)} = \frac{1}{6} \\ {x}^{2} - 25x + 150 = 0 \\ (x - 15)(x - 10) = 0 \\ x = 15 \: or \: 10$
Thus, one part is 10 and other part is 15

Answer 2

Thank you for asking this question.

f the first part = x

The second part = 25-x

Sum of reciprocals:

1/x + 1/25-x = 1/6

x² - 25x + 150 = 0

This is a quadratic equation

x = 10, x = 15

So, 25 can be split into 10 and 15

If there is any confusion please leave a comment below.