[tex]\displaystyle 2z-2x-2y=-20 \Leftrightarrow -2(x+y-z)=-20 \Rightarrow x+y-z=10. \\ \\ x^2-(y-z)^2=10^3 \\ \\ \Big(x+(y-z) \Big) \Big(x-(y-z) \Big)=10^3 \\ \\ \underbrace{(x+y-z)}_\mbox{=10}}(x-y+z)=10^3 \\ \\ \Rightarrow x-y+z= \frac{10^3}{10}=10^2 \longrightarrow patrat~perfect.[/tex]
