若正数x,y满足2x-3根号xy-2y=0,求x⼀y

2025-05-20 21:20:17
推荐回答(2个)
回答(1):

题目不很清楚哈,我理解是: 已知: x-(xy)^0.5-2y=0; 求: (2x-(xy)^0.5)/(y+2*(xy)^0.5); 由已知:(x/y)-(x/y)^0.5-2=0; [(X/y)^0.5-2][(x/y)^0.5+1]=0; (x/y)^0.5=2; 求等价于 [2(x/y)-(x/y)^0.5]/[1+2*(x/y)^0.5]=6/5;

回答(2):

将等式两边同除以y,得:2x/y-3√x/y-2=0
即2(√x/y)^2-3√x/y-2=0
即(√x/y-2)(2√x/y+1)=0
∴√x/y=2
∴x/y=4