已知x,y∈R+,且9x+y-xy=0,则x+y的最小值为
问题描述:
已知x,y∈R+,且9x+y-xy=0,则x+y的最小值为
答
9x+y-xy=0
x=y/(y-9)
x+y=y/(y-9)+y
=(y-9+9)/(y-9)+y
=1+9/(y-9)+y-9+9
=10+9/(y-9)+(y-9) a+1/a>=2
>=10+2*3
当y=6时有 最小值是16