Question

divide 8 into two parts such that the sum of their reciprocals is 8/15

Answer 1

Answer:

Step-by-step explanation:

Solution:

x + y = 8

x = 8 - y

1/x + 1/y = 8/15

(y + x) / xy = 8/15

15(x + y) = 8xy

15x + 15y = 8xy

15(8 - y) + 15y = 8y(8 - y)

120 - 15y + 15y = 64y - 8y^2

8y^2 - 64y + 120 = 0

y^2 - 8y + 15 = 0

(y - 5)(y - 3) = 0

y = {5, 3}

the numbers are 5 and 3

5 + 3 = 8

(1/5) + (1/3) = 8/15

(3 + 5) / 15 = 8/15

Please Mark as Brainliest.