若x,y,z属于R+,则(xy+yz)/(x^2+y^2+z^2)的最大值是帮个忙!

Question

若x,y,z属于R +,则(xy+ yz)/(x^2+ y^2+ z^2)的最大值是
帮个忙!

Answer 1

1.由于^2<=(x+y)／2即√x+√y<=√2*√(x+y)则K=√x+√y／√(x+y)<=√2*√(x+y)／√(x+y<=√2k的最大值为√22.令a=sinA,b=cosA（-pi《A《pi）ab=cosA*sinA=1\2sin2A又 -1=<1\2sin2A<=1则-1\2...