(2) Cauchy inequality is to get six squares.

The origin of Cauchy inequality;

Vector A. Vector b=| Vector a|| Vector b|cosx

x 1x2+y 1y2≤√[(x 1)^2+(y 1)^2]√[(x2)^2+(y2)^2]

[(x 1)^2+(y 1)^2].[(x2)^2+(y2)^2]≥(x 1x2+y 1y2)^2

The condition that the equal sign holds is x 1/x2=y 1/y2= real number.

To three-dimensional space, that is,

cauchy inequality

Here [(A 2) 2+(B 2) 2+(C 2) 2]. ( 1 2+ 1 2+ 1 2)≥[A 2. 1+。

So the maximum value of A 2+B 2+C 2 is √3.