How to solve $$ \begin{cases} abc=xyz\\ a+b+c=x+y+z\\ ab+bc+ac=xy+yz+xz\\ \end{cases} $$ ?
We have $$ ab+bc+ac=xy+yz+xz\implies abc+bc^2+ac^2=c(xy+yz+xz) $$ and $$ a+b+c=x+y+z\implies ac^2+bc^2+c^3=c^2(xy+yz+xz) $$ So $$ xyz-c^3 = c(xy+yz+xz)-c^2(xy+yz+xz). $$ But this is too difficult, could you please give me a better solution? Thanks.