Question

When the reciprocal of the larger of two consecutive even integers is subtracted from 4 times the reciprocal of the smaller, the result is 56. Find the integers.

Answer 1

Answer: No solution

Explanation:

1st number: x

2nd number: x + 2

• reciprocal of the larger is
  `(1)/(x+2)`

• 4 times the reciprocal of the smaller is 4
  `((1)/(x))`

• reciprocal of the larger of two consecutive even integers is subtracted from 4 times the reciprocal of the smaller is 4
  `((1)/(x))` -
  `(1)/(x+2)`

• the result is 56: 4
  `((1)/(x))` -
  `(1)/(x+2)` = 56

Solve the equation:

4
`((1)/(x))` -
`(1)/(x+2)` = 56

`(4(x(x + 2)))/(x)` -
`(1(x(x + 2)))/(x+2)` = 56(x(x + 2))

4x + 8 - x = 56x² + 112x

3x + 8 = 56x² + 112x

0 = 56x² + 109x - 8

Use the quadratic formula to solve:

x =
`(-109+/-11√(113))/(112)`

The result is NOT AN INTEGER so there is NO SOLUTION