Question 503739
the difference of the reciprocals of two consecutive odd numbers is 1/84. find the numbers.
**
let x=odd number
x+2 =consecutive odd number
..
(1/x)-(1/(x+2))=1/84
LCD:x(x+2)(84)
84(x+2)-84x=x(x+2)
84x+168-84x=x^2+2x
x^2+2x-168=0
(x+14)(x-12)=0
x=-14
x+2=-12
or
x=12
x+2=14
..
ans:
-14 and -12
or
12and 14
..
note: answers came out even consecutive numbers. You might want to check with another tutor or teacher.  Maybe I am missing something.