解方程组(xy+x+y+1)⼀(x+y+2)=2

2025-05-14 20:44:27
推荐回答(4个)
回答1:

(xy+x+y+1)/(x+y+2)=2 即(x+y+2)/(xy+x+y+1)=[(x+1)+(y+1)]/(x+1)(y+1)
=1/(x+1)+1/(y+1)=1/2
同理:1/(x+1)+1/(z+1)=1/3 1/(y+1)+1/(z+1)=1/4
所以:三式一加:2[1/(x+1)+1/(y+1))+1/(z+1)]=1/2+1/3+1/4=13/12
1/(x+1)+1/(y+1)+1/(z+1)=13/24
所以1/(z+1)=13/24-1/2=1/24,z=23
1/(y+1)=13/24-1/3=5/24,y=24/5-1=19/5
1/(x+1)=13/24-1/4=7/24,x=24/7-1=17/7

回答2:

???
xy+x+y+1=2x+2y+4
xy+x+y=2x+2y+3
xy=x+y+3
x=0
y=-3

回答3:

xy+x+y+1=2x+2y+4
xy+x+y=2x+2y+3
xy=x+y+3
x=0
y=-3

回答4: