x,y,z是三个不全为0的实数,求（xy+2yz)/(x+y+z)的最大值
问题描述：
x,y,z是三个不全为0的实数,求（xy+2yz)/(x+y+z)的最大值
答
x^2+(1/5)y^2>=(2/√5)xy (4/5)y^2+z^2>=(4/√5)yz 则x^2+y^2+z^2>=(2/√5)xy+(4/√5)yz=(2/√5)(xy+2yz) (xy+2yz)/(x^2+y^2+z^2)