Question 503739: the difference of the reciprocals of two consecutive odd numbers is 1/84. find the numbers. Found 3 solutions by edjones, lwsshak3, Northwestern2015:Answer by edjones(8007) (Show Source):
You can put this solution on YOUR website! 1/x - 1/(x+2) = 1/84
84(x+2)-84x=x(x+2) multiply each side by 84x(x+2)
84x+168-84x=x^2+2x
x^2+2x-168=0
(x-12)(x+14)=0
x=12, x=-14
The numbers are 12 and 14 or -14 and -12.
Both sets of numbers are even.
.
Ed
You can put this solution on YOUR website! 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.
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