SOLUTION: Find two consecutive number if the sum of their reciprocal is 7/12

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Question 1001818: Find two consecutive number if the sum of their reciprocal is 7/12
Answer by josgarithmetic(39626) About Me  (Show Source):
You can put this solution on YOUR website!
n and n+1 are the numbers.

1%2Fn%2B1%2F%28n%2B1%29=7%2F12

n and n+1 are the numbers.

1%2Fn%2B1%2F%28n%2B1%29=7%2F12
LCD is 12n(n+1), so multiply both sides by LCD.
12%28n%2B1%29%2B12n=7n%28n%2B1%29
12n%2B12%2B12n=7n%262%2B7n
24n%2B12=7n%5E2%2B7n
7n%5E2-17n-12=0

n=%2817%2B-+sqrt%2817%5E2%2B4%2A7%2A12%29%29%2F14
n=%2817%2B-+sqrt%28625%29%29%2F14
highlight_green%28highlight%28n=%2817%2B-+25%29%2F14%29%29

Either n=-8%2F14 OR n=3.
Obviously the acceptable value must be highlight%28n=3%29 for the first consecutive number, IF the numbers must be integers..

The numbers are 3 and 4
(For integer results)