2x^2+y^2+z^2≥2xy+4x+2z-5
∵2x^2+y^2+z^2-(2xy+4x+2z-5)
=x^2-2xy+y^2+x^2-4x+4+z^2-2z+1
=(x-y)^2+(x-2)^2+(z-1)^2≥0
∴2x^2+y^2+z^2≥2xy+4x+2z-5
2x^2+y^2+z^2≥2xy+4x+2z-5
∵2x^2+y^2+z^2-(2xy+4x+2z-5)
=x^2-2xy+y^2+x^2-4x+4+z^2-2z+1
=(x-y)^2+(x-2)^2+(z-1)^2≥0
∴2x^2+y^2+z^2≥2xy+4x+2z-5