WOLFRAM|DEMONSTRATIONS PROJECT

The Arithmetic-Geometric Mean Inequality (II)

​
a
1.5
b
3
The arithmetic-geometric mean inequality:
ab
≤
a+b
2
, for
a,b≥0
.
The yellow and green triangles are similar, so
b
L
=
L
a
. Therefore
2
L
=ab
,
L=
ab
, and the figure shows that
L≤
a+b
2
.