Question

已知正数x,y满足x+2y=1，则1/x+2/y的最小ŀ

Answer 1

9

1/x+2/y
=(1/x+2/y)*(x+2y)
=5+2x/y+2y/x
≥5+2√[(2x/y)*(2y/x)]
=5+2*2
=9
当2x/y=2y/x，即x=y=1/3时雀绝，取得最拦羡小值为简岁拍9

Answer 2

式子化为(x+2y)/x+2(x+2y)/y
=5+2y/x+2x/y
≥5+2√(2y/x)x(2x/y)
=9，当且仅当闷好宏…蚂册等号成立袜闹。