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Answer:
The geometric mean is the average of a set of numbers calculated by multiplying the numbers together and then taking the nth root of the product.
To find the geometric mean between two numbers, you can use the following formula:
Geometric Mean = √(a * b)
Where:
* a is the first number
* b is the second number
For example, to find the geometric mean between 14 and 81, you would calculate:
Geometric Mean = √(14 * 81) = √(1134) = 33.67
Here are the geometric means for the other pairs of numbers in the image:
* 256 and 1: Geometric Mean = √(256 * 1) = 16
* -32 and 4: Geometric Mean = √(-32 * 4) = -8
* 64 and 2xy: Geometric Mean = √(64 * 2xy) = 8√(2xy)
* 6 and luxy: Geometric Mean = √(6 * luxy) = √(6luxy)
Remember that the geometric mean is always a positive number, even if one of the original numbers is negative.