Given:
The number 12 is the geometric mean between 3 and a number x.
We need to determine the value of x.
Value of x:
Since, we know that the geometric mean is the square root of the product of two numbers.
Hence, we have;
[tex]Geometric \ mean= \sqrt{a \times b}[/tex]
where a and b are two positive numbers.
Substituting Geometric mean = 12, a = 3 and b = x, we get;
[tex]12= \sqrt{3 \times x}[/tex]
Squaring on both sides, we get;
[tex]12^2=3 \times x[/tex]
[tex]144=3\times x[/tex]
Dividing both sides of the equation by 3, we have;
[tex]48=x[/tex]
Thus, the value of x is 48.
