Question

设为x,y,z三个互不相等的数,且x+1/y=y+1/z=z=1/x,则xyz的值是

Answer 1

x-y=1/z-1/y=(y-z)/(yz) (1)

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

y-z=1/x-1/z=(z-x)/(xz) (3)

(1)*(2)*(3)

(x-y)(x-z)(y-z)=(y-z)(y-x)(z-x)/(x^2y^2z^2)

(y-x)(z-x)(y-z)=(y-z)(y-x)(z-x)/(x^2y^2z^2)

因x,y,互不相等,所以

x^2y^2z^2=1

xyz=1或xyz=-1