When the reciprocal of the larger of two consecutive even integers

Question

 is subtracted from 4 times the reciprocal of the smaller, the result is 5/6. Find the integers.

Answer 1

Translate the question into an equation:

[4/(2k)] - [1/(2k+2)] = 5/6

 

(4/k) - [1/(k + 1) = 5/3

 

3(4k + 4 -k) = 5k(k+1) => 12k + 12 - 3k = 5k² + 5k

5k² - 4k - 12 = 0

(5k + 6)(k-2) = 0

 

The negative root is extraneous and k =2.

The integers are 4 and 6.

 

You should check that they make sense in the original statement of the problem.