数学难题难两道

来源：百度知道 编辑：UC知道 时间：2024/05/27 10:40:42
x+(9/y)=3,y+(1/z)=3,则z+(1/x)的值为;

xy/(x+y)=1; yz/(y+z)=2; zx/(z+x)=3;则x=

1
x+(9/y)=3 X=3-9/Y=(3Y-9)/Y 1/X=Y/(3Y-9)
y+(1/z)=3 1/Z=3-Y Z=1/(3-Y)
则
z+(1/x)=1/(3-Y)+Y/(3Y-9)=(3-Y)/[3(3-Y)]=1/3
2
xy/(x+y)=1 XY=X+Y XY-X=Y (Y-1)X=Y X=Y/(Y-1)
yz/(y+z)=2 YZ=2Y+2Z YZ-2Z=2Y (Y-2)Z=2Y Z=2Y/(Y-2)
则
zx=2Y/(Y-2)*Y/(Y-1)=2Y方/[(Y-2)(Y-1)]
Z+X=2Y/(Y-2)+Y/(Y-1)=[2Y(Y-1)+Y(Y-2)]/[(Y-2)(Y-1)]
=(2Y方-2Y+Y方-2Y)/[(Y-2)(Y-1)]
=(3Y方-4Y)/[(Y-2)(Y-1)]
ZX/(Z+X)=3=2Y方/(3Y方-4Y)
6Y方-12Y=2Y方
4Y方-12Y=0 4Y(Y-3)=0 Y=0不要 Y=3
则
X=Y/(Y-1)=3/2