Đặt\(\frac{x}{2019}=\frac{y}{2020}=\frac{z}{2021}=k\Rightarrow\hept{\begin{cases}x=2019k\\y=2020k\\z=2021k\end{cases}}\)
Khi đó (x - y)2 = (2019k - 2020k)2 = (-k)2 = k2 (1)
\(\frac{\left(x-z\right)\left(y-z\right)}{2}=\frac{\left(2019k-2021k\right)\left(2020k-2021k\right)}{2}=\frac{\left(-2k\right).\left(-k\right)}{2}=\frac{2k^2}{2}=k^2\)(2)
Từ (1) và (2) => đpcm