Rozwiązanie:
[tex](x-y)^{2}+(y-z)^{2}+(z-x)^{2}=3x^{2}+3y^{2}+3z^{2}\\x^{2}-2xy+y^{2}+y^{2}-2yz+z^{2}+z^{2}-2xz+x^{2}=3x^{2}+3y^{2}+3z^{2}\\2x^{2}+2y^{2}+2z^{2}-2xy-2yz-2xz-3x^{2}-3y^{2}-3z^{2}=0\\-x^{2}-y^{2}-z^{2}-2xy-2yz-2xz=0\\x^{2}+y^{2}+z^{2}+2xy+2yz+2xz=0\\(x+y+z)^{2}=0\\0=0\\L=P[/tex]
co kończy dowód.
