Từ [tex][tex]x+y+z=0 \Rightarrow y+z=-x \Rightarrow (y+z)^{5}=-x^{5}[/tex]
[tex]\Rightarrow y^{5}+5y^{4}z+10y^{3}z^{2} +10y^{2}z^{3} +5yz^{4}+z^{5}=-x^{5}[/tex]
[tex]\Rightarrow (x^{5}+y^{5}+z^{5})+5yz(y^{3}+2y^{2}z+2yz^{2}+z^{3})=0[/tex]
[tex]\Rightarrow (x^{5}+y^{5}+z^{5}) +5yz\left [ (y+z)(y^{2}-yz+z^{2})+2yz(y+z) \right ]=0[/tex]
[tex]\Rightarrow (x^{5}+y^{5}+z^{5}) +5yz(y+z)(y^{2}+yz+z^{2})=0[/tex]
[tex]\Rightarrow 2(x^{5}+y^{5}+z^{5})-5xyz\left [ (y^{2}+2yz+z^2)+y^2+z^2 \right ]=0[/tex]
[tex]\Rightarrow 2(x^{5}+y^{5}+z^{5})=5xyz\left [ (y+z)^2 +y^2+z^2\right ][/tex]
Vậy [tex]: 2(x^{5}+y^{5}+z^{5}) = 5xyz(x^2+y^2+z^2)[/tex][/tex]