find two consecutive whole numbers, the difference of whose reciprocal is 1/12

Question

quadratic equation question.

Answer 1

The consecutive whole numbers can be called

x, x+1

 

The reciprocal of x = 1/x

The reciprocal of x+1 = 1/(x+1)

 

1/x - 1/(x+1) = 1/12

 

Get a common denominator on the left side

of x(x+1)

 

[(x+1) - x]/[x(X+1)] = 1/12

 

1/(x²+x) = 1/12

Cross multiply

x²+x=12

x²+x-12 = 0

(x+4)(x-3) = 0

 

X = -4 or x=3

 

Your consecutive whole numbers are

-4, -3  or  3, 4

 

You can plug that back into the equation

1/x - 1/(x+1) = 1/12 to verify.