若x,y这正整数,满足x分之4+y分之16=1,求x+y的最小值

问题描述:

若x,y这正整数,满足x分之4+y分之16=1,求x+y的最小值

4/x+16/y=1
x+y
=(x+y)(4/x+16/y)
=4+16(x/y)+4(y/x)+16
=20+16(x/y)+4(y/x)
因为 x,y这正整数
≥20+2√[16(x/y)*4(y/x)]
=20+2√64
=20+16
=36
所以
最小值为 36