Đáp án + giải thích các bước giải:
`1/x+1/y+1/z=1/(x+y+z)`
`->(yz+zx+xy)/(xyz)-1/(x+y+z)=0`
`->((yz+zx+xy)(x+y+z)-xyz)/(xyz(x+y+z))=0`
`->xyz+x^2z+x^2y+xyz+y^2x+y^2z+xyz+z^2x+z^2y-xyz=0`
`->x^2z+x^2y+y^2x+y^2z+z^2x+z^2y+2xyz=0`
`->xyz+y^2z+xz^2+yz^2+x^2y+xy^2+x^2z+xyz=0`
`->z(xy+y^2+zx+zy)+x(xy+y^2+xz+yz)=0`
`->(x+z)[y(x+y)+z(x+y)]=0`
`->(x+z)(z+y)(x+y)=0`
`->`\(\left[ \begin{array}{l}z=-x\\y=-z\\x=-y\end{array} \right.\)
`->`\(\left[ \begin{array}{l}z^8=x^8\\y^9=-z^9\\x^{10}=y^{10}\end{array} \right.\)
`->`\(\left[ \begin{array}{l}z^8-x^8=0\\y^9+z^9=0\\x^{10}-y^{10}=0\end{array} \right.\)
`->(z^8-x^8)(y^9+z^9)(x^10-y^10)=0`
`->M=3/4+0=3/4`
