WOLFRAM|DEMONSTRATIONS PROJECT

The Arithmetic-Geometric Mean Inequality (I)

​
a
3
b
2
The arithmetic-geometric mean inequality:
ab
≤
a+b
2
, for
a,b≥0
.
The figure shows that
2
(a+b)
-
2
(a-b)
=4ab
, therefore
ab
=
2
(a+b)
-
2
(a-b)
4
≤
2
(a+b)
4
=
a+b
2
.