`A=sqrt[1/(x-y)^2+1/(y-z)^2+1/(z-x)^2]`
`A^2=1/(x-y)^2+1/(y-z)^2+1/(z-x)^2`
`A^2=[(x-y)^2(y-z)^2+(y-z)^2(z-x)^2+(z-x)^2(x-y)^2]/[(x-y)^2(y-z)^2(z-x)^2`
`A^2=(x^2+y^2+z^2-xy-yz-xz)^2/[(x-y)(y-z)(z-x)]^2`
`A=(x^2+y^2+z^2-xy-yz-xz)/[(x-y)(y-z)(z-x)`
`⇒A∈Q`