Question

已知三个数x y z 满足 xy/x+y=-2,yx/y+x=4/3,zx/z+x=-4/3,则xyz/xy+xz+yz

Answer 1

题目有问题,yx/(y+x)=4/3应该是yz/(y+z)=4/3

xy/(x+y)=-2

(x+y)/(xy)=-1/2

1/x +1/y=- 1/2 (1)

yz/(y+z)=4/3

(y+z)/(yz)=3/4

1/y +1/z=3/4 (2)

zx/(z+x)=-4/3

(z+x)/(zx)=-3/4

1/x +1/z=-3/4 (3)

(1)+(2)+(3)

2(1/x+ 1/y+ 1/z)=-1/2

1/x +1/y +1/z=-1/4

xyz/(xy+yz+zx)=1/(1/x +1/y +1/z)=1/(-1/4)=-4