Answer:
We are supposed to find the arithmetic mean of 1, -x, and x².To find the arithmetic mean of any given set of numbers, we need to add all the given numbers and divide them by the total number of given numbers. Arithmetic Mean = (Sum of the given numbers) / (Total number of given numbers)So, the sum of 1, -x, and x² is given by,1 - x + x²Now, the total number of given numbers is 3. So, the arithmetic mean of 1, -x, and x² is,(1 - x + x²) / 3Therefore, the required arithmetic mean between 1, -x, and x² is (1 - x + x²) / 3.