2yz/x+2xz/y+2xy/z≥2x+2y+2z

来源:学生作业帮助网 编辑:六六作业网 时间:2024/10/06 17:52:22
2yz/x+2xz/y+2xy/z≥2x+2y+2z2yz/x+2xz/y+2xy/z≥2x+2y+2z2yz/x+2xz/y+2xy/z≥2x+2y+2zXYZ(2yz/x+2xz/y+2xy/z)

2yz/x+2xz/y+2xy/z≥2x+2y+2z
2yz/x+2xz/y+2xy/z≥2x+2y+2z

2yz/x+2xz/y+2xy/z≥2x+2y+2z
XYZ(2yz/x+2xz/y+2xy/z)/XYZ=(2Y^2Z^2+2X^2Y^2+2X^2Z^2)/XYZ
=(Y^2Z^2+X^2Y^2+X^2Z^2+Y^2Z^2+X^2Y^2+X^2Z^2)/XYZ
>=(2XYZ^2+2XZY^2+2YZX^2)/XYZ
=2X+2Y+2Z