SOLUTION: The sum of the reciprocals of two consecutive integers is 7/12. Find the two integers.

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Question 103393This question is from textbook intermediate algebra
: The sum of the reciprocals of two consecutive integers is 7/12. Find the two integers. This question is from textbook intermediate algebra

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1%2Fx%2B1%2F%28x%2B1%29=7%2F12
12x%2A%28x%2B1%29%2A%281%2Fx%2B1%2F%28x%2B1%29%29=12x%28x%2B1%29%2A7%2F12 Multiply both sides by 12x*(x+1) to remove all denominators.
12%28x%2B1%29%2B12x=7x%2A%28x%2B1%29Distributive property and simplify.
12x%2B12%2B12x=7x%5E2%2B7x Distributive property.
24x%2B12-24x-12=7x%5E2%2B7x-24x-12 Additive inverse of 24x+12
7x%5E2-17x-12=0
Use the quadratic equation,
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
where a=7, b=-17, and c=-12
x+=+%28-%28-17%29+%2B-+sqrt%28+17%5E2-4%2A7%2A%28-12%29%29%29%2F%282%2A7%29+
x+=+%2817+%2B-+sqrt%28+289%2B336%29%29%2F%2814%29+
x+=+%2817+%2B-+25%29%2F%2814%29+
x+=+42%2F14+ and x=-8%2F14
Since the answer we are looking for needs to be an integer choose
x=42%2F14 or x=3
Verify your answer.
1%2F3+%2B+1%2F4+=+7%2F12
4%2F12+%2B+3%2F12+=+7%2F12
7%2F12+=+7%2F12
Good answer
Two integers are 3 and 4.