Đáp án:
`min F = 1 <=> x=y=1, z =-1`
Giải thích các bước giải:
`F=2x^2 + 6y^2 + 5z^2 - 6xy + 8yz - 2xz + 2y + 4z +2`
`F = (2(6y^2 + 5z^2 + 8yz+ 2x^2 - 6xy - 2xz))/2+ 2 + 2y + 4z`
`F = (12y^2 + 10z^2 + 16yz + 4x^2 - 12xy - 4xz)/2 + 2 + 2y+ 4z`
`F = (2y^2 + 8z^2 + 8yz + 9y^2 + z^2 + 4x^2 + 6yz -12xy - 4xz + y^2 + 2yz + z^2)/2 + 2 + 2y + 4z`
`F = y^2 + 4z^2 + 2 + 4yz + 2y + 4z + (9y^2 + z^2 + 4x^2 + 6yz - 12xy - 4xz)/2 + (y^2 + 2yz + z^2)/2 `
`F = y^2 + 4z^2 + 1+ 4yz + 2y + 4z + (9y^2 + z^2 + 4x^2 + 6yz - 12xy - 4xz)/2 + (y^2 + 2yz + z^2)/2 +1`
`F = (y+ 2z +1)^2 + (3y+ z - 2x )^2/2 + (y+z)^2/2 +1 ge 1`
Vậy `min F = 1 <=> x=y=1, z =-1`
