Question

x,y>0且x+2y=3,则1/x+1/y的最小值?

Answer 1

题目：x、y>0,且x+2y=3,则1/x+1/y的最小值?

1/x+1/y

=1/3*(3/x+3/y)

=1/3*[(x+2y)/x+(x+2y)/y]

=1/3*[(1+2y/x)+(x/y+2)]

=1/3*(3+2y/x+x/y)

≥1/3*[3+2√(2y/x*x/y)]

=1/3*(3+2√2)

=(3+2√2)/3

当且仅当2y/x=x/y,即x=-3+3√2,y=(6-3√2)/2时,1/x+1/y获得最小值为：(3+2√2)/3.