A positive integer is 3 less than another. If the sum of the reciprocal of the smaller and twice the reciprocal of the larger is 9/20,

Question

find integers

 

Answer 1

x = y - 3

 

(1/x) + (2/y) = 9/20

[1/(y-3)] + (2/y) = 9/20

(3y - 6)/[y(y-3)] = 9/20

60y - 120 = 9y² - 27y

9y² - 87y + 120 =0

3y² - 29y + 40 = 0

Quadratic formula gives an extraneous root and y = 8 so that x = 5.

You should put these answers back into the original problem to make sure they work.