若x>0,y>0,且xy+x+2y=30,试求(1)xy的最大值.(2)x+2y的最小值

(1)F(x,y)=xy+a(xy+x+2y-30)
F`x=y+a(y+1)=0
a=-y/(y+1)
F`y=x+a(x+2)=0
a=-x/(x+2)
y/(y+1)=x/(x+2)
x=2y
xy+x+2y=30
2y^2+2y+2y=30
y=3 x=6
xy的最大值18
(2)F(x,y)=x+2y+a(xy+x+2y-30)
F`x=1+a(y+1)=0
F`y=2+a(x+2)=0
x=2y
x=6 y=3
x+2y的最小值=12