x+y-xy=-5
得到:xy-x-y=5
即:xy-x-y+1=6
分解因式:(x-1)(y-1)=6
同理:(y-1)(z-1)=8
(x-1)(z-1)=12
相乘得到
[(x-1)(y-1)(z-1)]的平方=576
(x-1)(y-1)(z-1)=±24
(1)(x-1)(y-1)(z-1)=24
分别除以上面三个式子,得到
x-1=3,解得x=4
y-1=2,解得y=3
z-1=4,解得z=5
(2)(x-1)(y-1)(z-1)= -24
分别除以上面三个式子,得到
x-1= -3,解得x= -2
y-1= -2,解得y= -1
z-1= -4,解得z= -3
x+y-xy=-5
y=(x+5)/(x-1)
x+z-xz=-11
z=(x+11)/(x-1)
y+z-yz=-7
(x+5)/(x-1)+(x+11)/(x-1)-(x+5)/(x-1)*(x+11)/(x-1)+7=0
(x+5)*(x-1)+(x+11)*(x-1)-(x+5)*(x+11)+7*(x-1)²=0
8x²-16x-64=0
x²-2x-8=0
x=4,x=-2
x=4,y=3,z=5
x=-2,y=-1,z=-3