Find the product of all real values of r for which 1/2x=r-x/7

Step-by-step explanation:

Given

Required

Find all product of real values that satisfy the equation

Cross multiply:

Subtract 7 from both sides

Reorder

Multiply through by -1

The above represents a quadratic equation and as such could take either of the following conditions.

(1) No real roots:

This possibility does not apply in this case as such, would not be considered.

(2) One real root

This is true if

For a quadratic equation

By comparison with

Substitute these values in

Add 56 to both sides

Divide through by 4

Take square roots

Hence, the possible values of r are:

or

and the product is: