Question

The sum of the reciprocals of two consecutive even integers is 7/24. write an equation that can be used to find the two integers. find the two integers.

a. ; 4 and 6

b. ; 6 and 8

c. ; 6 and 8

d. ; 4 and 6

Answer 1

To find the two consecutive even integers with a sum of reciprocals equal to 7/24, we can set up an equation and solve for the integers.

Step-by-step explanation:

To find the two consecutive even integers, we can set up an equation using the given information. Let x be the first even integer. The second even integer would be x+2. The sum of their reciprocals is 1/x + 1/(x+2). We are given that this sum is equal to 7/24. So, we can set up the equation 1/x + 1/(x+2) = 7/24. To solve this equation, we can multiply both sides by the common denominator of 24x(x+2) to eliminate the fractions. By simplifying the equation, we can find the value of x and then calculate the second even integer.

The correct answer is option a. 4 and 6.

Answer 2

Sorry that took so long. Calculator was having problems :). Here is how I did it
1/x + 1/(x+2) = 7/24
x+2/(x(x+2)) + x/(x(x+2)) = 7/24
2x+2/(x(x+2)) = 7/24
48x + 48 = 7x^2 + 14x
7x^2 - 34x - 48 = 0 next I used the quadratic formula program on my calculator
(x-6)(x+8/7) so the smaller of the numbers will be 6 and then since we know its the next even the other number will be 8. So 6, 8! Hope this helped