SOLUTION: The sum of the reciprocals of two consecutive positive integers is seventeen seventy-two. Write an equation that can be used to find the two integers. What are the integers?

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Question 703375: The sum of the reciprocals of two consecutive positive integers is seventeen seventy-two. Write an equation that can be used to find the two integers. What are the integers?
Answer by nshah11(47) About Me  (Show Source):
You can put this solution on YOUR website!
Note that since the integers are positive and consecutive, let them be represented by x and (x + 1).
Reciprocal of x => 1/x
Reciprocal of (x + 1) => 1/(x + 1)
1/x + 1/(x + 1) = 1772
Getting a common denominator of x(x + 1):
(x + 1) + x = 1772(x)(x + 1)
2x + 1 = 1772x^2 + 1772x
1772x^2 + 1770x - 1 = 0
Via the quadratic formula:
x = (-1770 +/- √(1770^2 - 4(1772)(-1))/(2*1772) yields no integers at all. Pleas recheck your problem.