Question

If xy = 1 what is the arithmetic mean of x and y in terms of y? Please show work as detailed as possible

Answer 1

(1+y^2) /2y

Explanation:

arithmetic mean is the average of x and y

(x+y)/2

Using the equation

xy = 1

and solving for x

x = 1/y

Replacing x in the first equation

(1/y + y) /2

Multiply by y/y

(1/y + y) /2 * y/y

(1/y + y)*y /2y

(1+y^2) /2y