设x.y.z.是3个不全为0的实数,求xy+2yz/x.x+y.y+z.z的最大值

问题描述:

设x.y.z.是3个不全为0的实数,求xy+2yz/x.x+y.y+z.z的最大值

由(xy+2yz)/(x²+y²+z²)令x=0,得:2yz/(y²+z²)(1)∵(y-z)²≥0,∴y²-2yz+z²≥0,即y²+z²≥2yz(2)∴(1)式为2yz/(y²+z²)≤1,当且仅当x=0,y=z≠...