SOLUTION: The sum of the reciprocals of two consecutive odd integers is 8/15. Find the integers. Thank you.

Algebra.Com
Question 55652: The sum of the reciprocals of two consecutive odd integers is 8/15. Find the integers. Thank you.
Answer by aaaaaaaa(138)   (Show Source): You can put this solution on YOUR website!
reciprocal of x = the number which multiplied by x gives 1.
Therefore, we can express the reciprocal of x as .
So now, let's assign the variables to the values:
First number = 2x+1
Second number = 2x+3
Reciprocal of first =
Reciprocal of second =
The assugnment of the two numbers requires ome explanation. As the problem requires the two numbers to be odd, we use a little trick (that 2x is always even), to determine that 2x+1 and 2x+3 will be always odd.

Take the lcm of the denominators (it's ):




Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=4624 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 1, -1.125. Here's your graph:


Since 1.125 is not an integer, x = 1, first = 3 and second = 5.
RELATED QUESTIONS

The sum of the reciprocals of 2 consecutive odd integers is 8/15. Find the... (answered by josgarithmetic,MathTherapy)
The sum of the reciprocals of two consecutive odd integers is 8/15.Find the larger... (answered by checkley75)
The sum of the reciprocals of two odd integers is 8/15. Find the larger integer. (answered by ankor@dixie-net.com)
The sum of the reciprocals of two consecutive odd integers is 8/15. Find the integers. (answered by Alan3354,josgarithmetic)
the sum of the reciprocals of two consecutive odd integers is 20/99. find the two... (answered by Alan3354)
The sum of the reciprocals of two consecutive odd integers is 20/90. Find the two... (answered by edjones)
The sum of the reciprocals of two consecutive odd integers is 20/99. Find the two... (answered by palanisamy,edjones)
The sum of the reciprocals of two consecutive odd integers is 8/15 (which is a fraction). (answered by user_dude2008)
. The sum of the reciprocals of two consecutive positive odd integers is 16/63. Find the... (answered by ewatrrr,stanbon)