`4x^2 + 2y^2 + 2z^2 - 4xy - 4xz + 2yz - 6y - 10z + 34 = 0`
`<=> 4x^2 - 4x(y + z) + (y^2 + 2yz + z^2) + (y^2 - 6y + 9) + (z^2 - 10z + 25) = 0`
`<=> (2x)^2 - 2. 2x(y + z) + (y + z)^2 + (y - 3)^2 + (z - 5)^2 = 0`
`<=> (2x - y - z)^2 + (y - 3)^2 + (z - 5)^2 = 0`
`<=> x = 4, y = 3, z = 5`
Thay `x = 4, y = 3, z = 5` vào tổng `S`, ta được:
`S = (4 - 4)^2020 + (3 - 4)^2020 + (5 - 4)^2020`
`= 0 + 1 + 1`
`= 2`
Vậy `S = 2`