Lời giải:
$y^2=36-8(x-2024)^2\leq 36$ (do $8(x-2024)^2\geq 0$)
$\Rightarrow y\leq 6$
Lại có: $y^2=36-8(x-2024)^2$ chẵn nên $y$ chẵn
$\Rightarrow y\in\left\{0; 2; 4; 6\right\}$
Nếu $y=0$ thì $8(x-2024)^2=36$
$\Rightarrow (x-2024)^2=\frac{36}{8}\not\in\mathbb{N}$ (loại)
Nếu $y=2$ thì $8(x-2024)^2=36-y^2=36-2^2=32$
$\Rightarrow (x-2024)^2=4\Rightarrow x-2024=\pm 2$
$\Rightarrow x=2026$ hoặc $x=2022$ (tm)
Nếu $y=4$ thì $8(x-2024)^2=36-4^2=20$
$\Rightarrow (x-2024)^2=\frac{20}{8}\not\in\mathbb{N}$ (loại)
Nếu $y=6$ thì $8(x-2024)^2=36-6^2=0$
$\Rightarrow x-2024=0$
$\Rightarrow x=2024$ (tm)
Vậy............