Question 68667
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 of this: ratical 24 is the geometric mean between a and b. Find b if a=2
Geometric Mean = {{{sqrt(ab)}}}
{{{24 = sqrt(2b)}}}
<br>{{{24^2 = sqrt(2b)^2}}}
<br>{{{576 = 2b}}}
<br>{{{highlight (b= 288)}}}
<br>
Checking:
Geometric Mean = {{{sqrt(ab)}}}, GM = 24, a = 2, b = 288<br>
{{{24 = sqrt(2*288)}}}
<br>{{{24 = sqrt(576)}}}
<br>24=24 ---> True