MATH SOLVE

5 months ago

Q:
# The sum of the reciprocals of two consecutive odd integers is 24/143. find the two integers.

Accepted Solution

A:

let one integer be x, the consecutive odd integer is x+2

reciprocals are 1/x and 1/(x+2)

1/x +1/(x+2)=24/143

make the denominators the same:

(x+2)/[x(x+2)] +x/[x(x+2)]=24/143

143(2x+2)=24(x)(x+2)

286x+286=24x²+48x

24x²-238x-286=0

use the quadratic formula: x=22 this doesn't work because 22 is not an odd number.

or x=-2.1666666666 (this is not an integer)

weird.

reciprocals are 1/x and 1/(x+2)

1/x +1/(x+2)=24/143

make the denominators the same:

(x+2)/[x(x+2)] +x/[x(x+2)]=24/143

143(2x+2)=24(x)(x+2)

286x+286=24x²+48x

24x²-238x-286=0

use the quadratic formula: x=22 this doesn't work because 22 is not an odd number.

or x=-2.1666666666 (this is not an integer)

weird.