Đáp án: $\dfrac{2026}{2025}$

Giải thích các bước giải:

Ta có:

$y=\dfrac{x^2}{x^2-2x+2026}$

$\to y-\dfrac{2026}{2025}=\dfrac{x^2}{x^2-2x+2026}-\dfrac{2026}{2025}$

$\to y-\dfrac{2026}{2025}=\dfrac{-x^2+4052x-4104676}{2025\left(x^2-2x+2026\right)}$

$\to y-\dfrac{2026}{2025}=\dfrac{-(x-2026)^2}{2025\left(x^2-2x+2026\right)}\le 0$

$\to y\le \dfrac{2026}{2025}$

 $\to GTLN=\dfrac{2026}{2025}\to x=2026$