satisfy that: 
,![\[
\sqrt{a + b} + \sqrt{b + c} + \sqrt{c + a} \geq \frac{4(ab + bc + ca)}{\sqrt{(a + b)(b + c)(c + a)}}
\]](http://latex.artofproblemsolving.com/e/7/2/e72fd0f134289c359bc8766440babc52ae131961.png)
satisfied 
Find the minimum of 
Y by
Point 
lies on the sphere circumscribed around a cube. Prove that sum of squares of distances of point from the vertices of the cube does not depend on the choice of point .
lies on the sphere circumscribed around a cube. Prove that sum of squares of distances of point from the vertices of the cube does not depend on the choice of point .
vertices equals 
times the square of the space diagonal, or 
,
is the side length of the cube.
