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