Show that the geometric mean, radical(ab), is always less than or equal to the arithmetic mean, (a+b)/2.
Hello, Slazenger3!
Show that the geometric mean, , is always less than or equal to the arithmetic mean,
For any two real numbers, and : .
We have: .
Add to both sides: .
Then we have: /
Divide by 4: .
Take square root: .
Therefore, the arithmetic mean is always greater than or equal to the geometric mean.