Question

the difference of two number is 5 and the difference their reciprocal is 1 by 10 find the number

Answer 1

ohh its so simple question.you just need to simplify the given conditions, then you will get it. And the answer is 10 and 5

Answer 2

Let the required numbers be x and x+5
According to the question
$\frac{1}{x} - \frac{1}{x + 5} = \frac{1}{10} \\ \frac{x + 5 - x}{x(x + 5)} = \frac{1}{10} \\ \frac{ 5}{ {x}^{2} + 5x } = \frac{1}{10} \\ 50 = {x}^{2} + 5x \\ {x }^{2} + 5x - 50 = 0 \\ {x}^{2} + 10x- 5x - 50 = 0 \\ x(x + 10) - 5(x + 10) = 0 \\ (x - 5)(x + 10) = 0 \\ x - 5 = 0 \\ x = 5 \\ and \\ x + 10 = 0 \\ x = - 10 \\ if \: x = 5 \: then \: \: second \: number = > x + 5 = 5 + 5 = 10 \\ if \: x = - 10 \: then \: second \: number = > \: x + 5 = - 10 + 5 = - 5$