x+2y = 1
(x+2y)*(1/x + 1/y) = 1+2 + 2y/x + x/y
令x/y = a
2y/x + x/y = a + 2/a
由均值不等式得,当a = √2时,2/a + a取到最小值为2√2
所以1/x+1/y的最小值为3+2√2