Cho `x+y+z=0` c/m `x^3+y^3+z^3=3xyz`

~ Bạn tham khảo ~

`x + y + z = 0`

`<=> (x + y + z)(x^2 + y^2 + z^2 - xy - yz - xz) = 0`

`<=> (x + y + z)(x^2 + 2xy + y^2 - z(x + y) + z^2 - 3xy) = 0`

`<=> (x + y + z)[ (x + y)^2 - z(x+ y) + z^2] - 3xy(x + y + z) = 0`

`<=> (x + y)^3 + z^3 - 3xy(x + y) - 3xyz = 0`

`<=> x^3 + y^3 + 3xy(x + y) - 3xy(x + y) + z^3 = 3xyz`

`<=> x^3 + y^3 + z^3 = 3xyz` (đpcm)