Ta có:
`a/x+b/y+c/z=0`
`⇒ayz+bxz+cxy=0`
Ta có:
` x/a+y/b+z/c=1`
`⇔(x/a+y/b+z/c)^2=1`
`⇔x^2/a^2+y^2/b^2+z^2/c^2+2((xy)/(ab)+(yz)/(bc)+(zx)/(ca))=1`
`⇔x^2/a^2+y^2/b^2+z^2/c^2+2((ayz+bxz+cxy)/(abc))=1`
`⇔x^2/a^2+y^2/b^2+z^2/c^2+2.0=1`
`⇔x^2/a^2+y^2/b^2+z^2/c^2=1`
`⇒ĐPCM`