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

Step-by-step explanation:

1st number: x

2nd number: x + 2

• reciprocal of the larger is $\frac{1}{x+2}$

• 4 times the reciprocal of the smaller is 4$(\frac{1}{x})$

• reciprocal of the larger of two consecutive even integers is subtracted from 4 times the reciprocal of the smaller is 4$(\frac{1}{x})$ - $\frac{1}{x+2}$

• the result is 56: 4$(\frac{1}{x})$ - $\frac{1}{x+2}$ = 56

Solve the equation:

4$(\frac{1}{x})$ - $\frac{1}{x+2}$ = 56

$\frac{4(x(x + 2))}{x}$ - $\frac{1(x(x + 2))}{x+2}$ = 56(x(x + 2))

4x + 8 - x = 56x² + 112x

     3x + 8 = 56x² + 112x

             0 = 56x² + 109x - 8

Use the quadratic formula to solve:

x = $\frac{-109+/-11\sqrt{113}}{112}$

The result is NOT AN INTEGER so there is NO SOLUTION