Find the Arithmetic Mean between (a − b) and (a + b)?

Given:

Two numbers: x = a - b and y = a + b

Concept used:

The arithmetic mean (average) between two numbers x and y is given by:

Arithmetic Mean = \(\dfrac{x + y}{2}\)

Calculation:

Using the given values of x and y:

Arithmetic Mean = \(\dfrac{(a - b) + (a + b)}{2}\)

Simplifying the expression in the numerator:

Arithmetic Mean = \(\dfrac{2a}{2}\)

Canceling out the common factor of 2:

Arithmetic Mean = a

∴ The arithmetic mean between a - b and a + b is a.