Question

设x,y,z是正实数,则(xy+2yz)/(x平方+y平方+z平方)的最大值为

Answer 1

x、y、z∈R+，由于xy+2yz ≤(x²+y²)/2+(y²+z²)=(x²+3y²+2z²)/2，那么

(xy+2yz)/(x²+y²+z²)≤(x²+3y²+2z²)/(2x²+2y²+2z²)