Explicație pas cu pas:
Pornim de la :
(Vx-Vy)²>=0
(Vx-Vz)²>=0
(Vy-Vz)²>=0
Adica:
x+y>=2Vxy
x+z>=2Vxz
y+z>=2Vyz
Le adunam:
x+y+x+z+y+z>=2Vxy+2Vxz+2Vyz =>
2x+2y+2z>=2(Vxy+Vxz+Vyz)=>
2(x+y+z)>=2(Vxy+Vxz+Vyz)=>
x+y+z>=Vxy+Vxz+Vyz (q.e.d)
Met 2
x+y+z>=Vxy+Vxz+Vyz /*2 =>
2x+2y+2z>=2Vxy+2Vxz+2Vyz =>
2x+2y+2z-2Vxy-2Vxz-2Vyz>=0 =>
x-2Vxy+y+x-2Vxz+z+y-2Vyz+z>=0 =>
(Vx-Vy)²+(Vx-Vz)²+(Vy-Vz)²>=0 (A) q.e.d
