2x+8y-xy=0 2x+8y=xy 2/y + 8/x=1 x+y =2x+8y-xy=02x+8y=xy2/y + 8/x=1x+y=(x+y)*1=(x+y)(2/y + 8/x)=8+2+ 2x/y +8y/x≥10+2√[(2x/y)(8y/x)]=10+2√16=18最小值为18没看懂的地方=8+2+ 2x/y +8y/x≥10+2√[(2x/y)(8y/x)]=10+2√16=18 2x/y +8y/x怎么算的等于2√[(2x/y)(8y/x)],又等于2√16
问题描述：
2x+8y-xy=0 2x+8y=xy 2/y + 8/x=1 x+y =
2x+8y-xy=0
2x+8y=xy
2/y + 8/x=1
x+y
=(x+y)*1
=(x+y)(2/y + 8/x)
=8+2+ 2x/y +8y/x
≥10+2√[(2x/y)(8y/x)]
=10+2√16=18
最小值为18
没看懂的地方=8+2+ 2x/y +8y/x
≥10+2√[(2x/y)(8y/x)]
=10+2√16=18
2x/y +8y/x怎么算的等于2√[(2x/y)(8y/x)],又等于2√16
答
2x/y +8y/x>=2√[(2x/y)(8y/x)]=2√16
运用了
a+b.>=2√(ab )