Question

If the sum of two consecutive integers is 15 if the sum of their resiprocal is 3/10 find the number

Answer 1

let the two numbers be x and y

so , x + y = 15 ----(1)

1/x + 1/y = 3/10

x + y /xy = 3/10

x + y = 3xy/10 ----- (2)

from eq 1 and eq 2

3xy/10 = 15

xy = 50

x = 50/y

putting this in eq 1

50/y + y = 15

50 + y^2 / y = 15

50 + y^2 = 15y

y^2 - 15y + 50 = 0

y^2 - 10y - 5y + 50 = 0

y(y -10) -5(y-10) = 0

(y-10) (y-5) = 0

(y-10) =0 or (y-5) = 0

y=10 or y = 5

the two numbers are 10 and 5