Question

若x>0,y>0,且x-根号下xy-2y=0,求【2x-根号下xy】÷【y+2根号下xy】的值

若x>0,y>0,且x-根号下xy-2y=0,求【2x-根号下xy】÷【y+2倍根号下xy】的值

Answer 1

x-√(xy)-2y=(√x-2√y)(√x+√y)=0
因为x>0,y>0
所以√x+√y>0
所以√x=2√y
x=4y
2x=8y,√(xy)=2√y*√y=2y

原式=(8y-2y)÷(y+4y)=6y/5y=6/5