Question

x,y,z>0,x(x+y+z)=10,求2x+y+z的最小值

Answer 1

因为x,y,z>0,所以

2x+y+z=x+(x+y+z)≥2*[x(x+y+z)]^(1/2)=2*√10,

等号当且仅当x=(x+y+z)=√10时成立.

故2x+y+z的最小值为2√10.