If x + y denotes the geometric mean of x and y, x ∗ y denotes the product of x and y, and (x, y) denotes the average of x and y, find (5 ∗ 4, 2 + 8).

Question

If x + y denotes the geometric mean of x and y, x ∗ y denotes the product of x and y, and (x, y) denotes the average of x and y, find (5 ∗ 4, 2 + 8).

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Solution

Sure, let's break it down:

First, we need to calculate the values for 5 ∗ 4 and 2 + 8.

5 ∗ 4 = 20 (This is the product of 5 and 4)

2 + 8 = √(2*8) = √16 = 4 (This is the geometric mean of 2 and 8)
Now, we substitute these values into the (x, y) operation, which denotes the average of x and y. So, we need to find the average of 20 and 4.

(20, 4) = (20 + 4) / 2 = 24 / 2 = 12

So, (5 ∗ 4, 2 + 8) = 12.

This problem has been solved

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