Question

已知三个数x,y,z满足x+y分之xy=负2,y+z分之yz=3分之4,z+x分之zx=负3分之4,求xy+yz+zx分

Answer 1

【x+y】分之xy=-2,

xy分之【x+y】=-1/2

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

【y+z】分之yz=3分之4,

yz分之【y+z】=3/4

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

【z+x】分之zx=-3分之4,

zx分之【z+x】=-3/4

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

(1)+(2)+(3),

得,2(1/x+1/y+1/z)= -1/2

则,1/x+1/y+1/z = -1/4

即,xyz分之 【xy+yz+zx】= -1/4

所以,【xy+yz+zx】分之xyz =-4