Question 68670
The Geometric Mean between any two positive numbers a and b is the square root of their product.
<br> If we are looking for positive geometric mean {{{sqrt(ab)}}}
<br> If we are looking for negative geometric mean {{{-sqrt (ab)}}}

<br><br>find the other extreme: ratical 12 is the gepmetric mean between a and b. Find b if a = 3.
Geometric Mean = {{{sqrt(ab)}}}
{{{12 = sqrt(3b)}}}
<br>{{{12^2 = sqrt(3b)^2}}}
<br>{{{144 = 3b}}}
<br>{{{highlight (b=48)}}}
<br>
Checking:
Geometric Mean = {{{sqrt(ab)}}}, GM = 12, a = 3, b = 48
<br>{{{12 = sqrt(3*48)}}}
<br>{{{12 = sqrt(144)}}}
<br>12=12 ---> True