Question

The difference between two positive numbers x and y is 4 and the difference between their reciprocals is 4/21. Find the numbers.

Answer 1

Step-by-step explanation:

hope you get it.........

Answer 2

Step-by-step explanation:

$x - y = 4 \: ...(1) \\ \\ \frac{1}{y} - \frac{1}{x} = \frac{4}{21} \: ....(2) \\ \\ on \: solving \: equation \: (2) \\ \\ = > \frac{x- y}{xy} = \frac{4}{21} \\ \\ = > \frac{ 4}{xy} = \frac{4}{21} \\ \\ = > xy = 21 \\ \\ = > x = \frac{ 21}{y} \\ \\ on \: putting \: the \: value \: of \: x \: in \: equation \: (1) \\ \\ = > \frac{ 21}{y} - y = 4 \\ \\ = > 21 - {y}^{2} = 4y \\ \\ = > {y}^{2} + 4y - 21 = 0 \\ \\ = > {y}^{2} + 7y - 3y - 21 = 0 \\ \\ = > y(y + 7) - 3(y + 7) = 0 \\ \\ = > (y + 7)(y - 3) = 0 \\ \\ y = 3 \: and \: - 7$

when y = -7 then, x = 4-7 = -3

when y = 3 then, x = 4+3 = 7