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<u>Given</u>:
The number 12 is the geometric mean between 3 and a number x.
We need to determine the value of x.
<u>Value of x:</u>
Since, we know that the geometric mean is the square root of the product of two numbers.
Hence, we have;
where a and b are two positive numbers.
Substituting Geometric mean = 12, a = 3 and b = x, we get;
Squaring on both sides, we get;
Dividing both sides of the equation by 3, we have;
Thus, the value of x is 48.