Đặt `A = x^2 + y^2 + z^2 - yz - 4x - 3y + 2027`

`A = x^2 - 4x + 4 + z^2 - zy + 1/4y^2 + 3/4y^2 - 3y + 3 + 2021`

`A = ( x - 2 )^2 + ( z - 1/2y )^2 + 3( 1/4y^2 - y + 1 ) + 2021`

`A = ( x - 2 )^2 + ( z - 1/2y )^2 + 3( 1/2y - 1 )^2 + 2021`

`Do  ( x - 2 )^2 >= 0  AA  x ; ( z - 1/2y )^2 >= 0  AA y ; z ; 3( 1/2y - 1 )^2 >= 0  AA  y`

`A = ( x - 2 )^2 + ( z - 1/2y )^2 + 3( 1/2y - 1 )^2 + 2021 >= 2021  AA  x ; y ; z`

`Dấu = xảy  ra:  {(( x - 2 )^2 = 0 ),(( z - 1/2y)^2 = 0 ),(3( 1/2y - 1 )^2 = 0 ):}`

`{( x - 2 = 0 ),( z - 1/2y = 0 ),( 1/2y - 1 = 0 ):}`

`{( x = 2 ),( z = 1 ),( y = 2 ):}`

`Vậy  A min = 2021` khi `( x ; y ; z ) = ( 2 ; 2 ; 1 )`