Question

the sum of two numbers is 8 and sum of their reciprocals is 8/5 find the numbers

Answer 1

Let number be x and (8-x)
1/x + 1/(8-x)=8/5
(8-x)/(8x-x^2) + x/(8x-x^2) =8/5
8/(8x-x^2) =8/5
5=8x - x^2
Then do quadratic for x^2 - 8x + 5