the sum of the reciprocals of two consecutive integers is -15/56.

Question

 find the two integers

Answer 1

 Two consecutive integers are 1/x and 1/ (x+1)

1/x + 1/ (x+1) = -15/56

(x+1+x)/x(x+1) = -15/56

56(x+1+x) = - 15 x( x+1)

56x+56+56x = -15x²- 15x

15x²+ 127x+ 56 = 0

Apply quadratic formula -b± √b²- 4ac/ 2a

= -127± √(127)²- 4( 15)(56)/2(30)

= - 127± √ 12769/ 30

= -127± 113/30

=( -127+113)/30 and ( -127-113)/30

Therefore x1= -14/30 = -7/15 and x2 = -8

The 2 consecutive integers are x1= -7/15 ( not an integer ) and x2 = - 8

Comments

The two consecutive integers are x and x+1 and its reciprocals are 1/x and 1/(x+1).

Solve 1/x + 1/(x+1) = -15/56 for x.

x = - 7/15 and x = -8

Here - 7/15 is not an integer, so the value of x = -8.

The two consecutive integers are x = - 8 and x+1 = -8+1 = - 7.