Sum of reciprocals of integers is given - find integers

[jackleyt]

Homework Statement

The sum of the reciprocals of two consecutive odd integers is 28/195. Find the two integers.

Homework Equations

?

The Attempt at a Solution

28/195= 1/x + 1/(x-2)
Solved using quadratic formula and got 3.44, which does not seem to be right.. Any help?

 

[symbolipoint]

Homework Statement

The sum of the reciprocals of two consecutive odd integers is 28/195. Find the two integers.

Homework Equations

?

The Attempt at a Solution

28/195= 1/x + 1/(x-2)
Solved using quadratic formula and got 3.44, which does not seem to be right.. Any help?

"Two consecutive odd integers...", you have then two numbers to start with:
2n+1, and 2n+3. The 'n' is a variable and the factor of 2 ensures that the entire expression will be ODD. Note that 'n' will be an integer.

 

[HallsofIvy]

Using "x" and "x-2" is just as valid as "2n+3" and "2n+1" so the equation you have, 1/x+ 1/(x-2)= 28/195 is perfectly good. Unfortunately, you have left out the important part: you don't show how you got 3.44. 1/x+ 1/(x-2)= 28/195, after you multiply the entire equation by 195x(x-2) becomes a quadratic formula and I get two integer solutions.