Does there exist a pair of consecutive integers whose reciprocals sum to 3/4? explain how you know.

NO

Step-by-step explanation:

Let the consecutive numbers be x and x + 1

Given condition is their reciprocals sum is equal to 3/4

Find the discriminant for the above quadratic equation

Foe a given quadratic equation the discriminant =

Here a = 3,b = -5,c = -4

Discriminant = =78 >0

If a quadratic equation has discriminant > 0 it has distinct real roots

The roots are and  

Here the roots are

They are not integers So there are no consecutive pair of integers which follow the given condition

step-by-step explanation:

what "following statement"?

step-by-step explanation: