Ta có:
`a+b+c=0`
`\to (a+b+c)(ax+by+cz)=0`
`⇔a^2x+aby+acz+abx+b^2y+bcz+acx+bcy+c^2z=0`
`⇔a^2x+b^2y+c^2z+(aby+abx)+(acz+acx)+(bcz+bcy)=0`
`⇔a^2x+b^2y+c^2z+ab(x+y)+ac(z+x)+bc(z+y)=0` `(1)`
Vì `x+y+z=0`
`\to x+y=-z;x+z=-y;y+z=-x` `(2)`
Từ `(1)` và `(2)`
`\to a^2x+b^2y+c^2z-abz-acy-bcx=0`
`⇔a^2x+b^2y+c^2z-(bcx+acy+abz)=0`
`⇔a^2x+b^2y+c^2z-((abcx)/a+(abcy)/b+(abcz)/c)=0`
`⇔a^2x+b^2y+c^2z-abc(x/a+y/b+z/c)=0`
Mà `x/a+y/b+z/c=0`
`to a^2x+b^2y+c^2z-abc.0=0`
`→ a^2x+b^2y+c^2z=0`
`→đpcm`
