3(y-2)^2-(2y+z)(-z+2y)

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3(y-2)^2-(2y+z)(-z+2y)3(y-2)^2-(2y+z)(-z+2y)3(y-2)^2-(2y+z)(-z+2y)当-1≤x≤2,-1≤y≤2,-1≤z≤3时原方程成立,∴当x=-1

3(y-2)^2-(2y+z)(-z+2y)
3(y-2)^2-(2y+z)(-z+2y)

3(y-2)^2-(2y+z)(-z+2y)
当-1≤x≤2,-1≤y≤2,-1≤z≤3时原方程成立,
∴当x=-1,y=-1,z=-1时,x+2y+3z值最小,x+2y+3z=-6
当x=2,y=2,z=3时,x+2y+3z值最大,x+2y+3z=15.

3(y-2)^2-(2y+z)(-z+2y)
=3(y-2)^2+(2y+z)(2y-z)
=3(y-z)^2+4y^2-z^2
=3y^2-6yz+3z^2+4y^2-z^2
=7y^2-6yz+2z^2