The Arithmetic-Geometric Mean Inequality (I)
The Arithmetic-Geometric Mean Inequality (I)
The arithmetic-geometric mean inequality: , for .
ab
≤a+b
2
a,b≥0
The figure shows that -=4ab, therefore -≤=.
2
(a+b)
2
(a-b)
ab
=2
(a+b)
2
(a-b)
4
2
(a+b)
4
a+b
2