# The Arithmetic-Geometric Mean Inequality (II)

The Arithmetic-Geometric Mean Inequality (II)

The arithmetic-geometric mean inequality: , for .

ab

≤a+b

2

a,b≥0

The yellow and green triangles are similar, so =. Therefore =ab, , and the figure shows that .

b

L

L

a

2

L

L=

ab

L≤

a+b

2