Question

Sum of two numbers is 8 . If the sum of their reciprocal is 8/15 find the numbers

Answer 1

let the numbers be x and 8-x

given

$\frac{1}{x} + \frac{1}{8 - x} = \frac{8}{15} \\ \\ \frac{8 - x + x}{x(8 - x)} = \frac{8}{15} \\ \\ {x}^{2} - 8x + 15 = 0 \\ \\ {x}^{2} - 3x - 5x + 15 = 0 \\ \\ x(x - 3) - 5(x - 3) = 0 \\ \\ (x - 3)(x - 5) = 0 \\ \\ x = 3 \\ \\ x = 5$

Therefore the numbers are 3 and 5.

hope it helps.