已知 X大于0,Y大于0,且X-根号XY-2Y=0,求2X-根号XY除以Y+2根号XY的值

问题描述:

已知 X大于0,Y大于0,且X-根号XY-2Y=0,求2X-根号XY除以Y+2根号XY的值

由x-√xy-2y=0可知,(√x+√y)(√x-2√y)=0
解得√x=2√y,即x=4y
则(2x-√xy)/(y+2√xy)=(2x-2y)/(y+4y)=6/5