已知xy/x+y=3,yz/y+z=2,xz/x+z=1,求x,y,z的值

Question

已知xy/x+y=3,yz/y+z=2,xz/x+z=1,求x,y,z的值

Answer 1

已知xy/(x+y)=3,yz/(y+z)=2,xz/(x+z)=1,求x,y,z的值
xy=3x+3y.(1)；yz=2(y+z).(2)；xz=x+z.(3)
由(3)得z=x/(x-1).(4)
将(4)代入(2)式得xy/(x-1)=2[y+x/(x-1)]=2[y(x-1)+x]/(x-1),消去分母得xy=2(xy-y+x)；
化简得xy=-2x+2y.(5)；
(1)-(5)得5x+y=0,故y=-5x；代入(5)得-5x²=-2x-10x,即有5x²-12x=x(5x-12)=0,
故x=12/5；或x=0(舍去)；
故x=12/5,y=-12；z=(12/5)/(12/5-1)=12/7.