试比较5x²+y²+z²与2xy+4x+2z-2

分类: 作业答案 • 2022-03-05 13:51:23

问题描述：

答

5x^2+y^2+z^2-(2xy+4x+2z-2)
=5x^2+y^2+z^2-2xy-4x-2z+2
=(4x^2-4x+1)+(x^2-2xy+y^2)+(z^2-2z+1)
=(2x-1)^2+(x-y)^2+(z-1)^2>=0
5x^2+y^2+z^2>=2xy+4x+2z-2