`\color{#00EDFF}{circ} \color{#1AD5F7}{H} \color{#1AD5F7} {e} \color{#4DA6E6}{r} \color{#668EDD}{e} \color{#8077D5} {n} \color{#995FCD}{a}`

`a) ( x - 1 )/2025 + ( x - 2 )/2024 = ( x - 3 )/2023 + ( x - 4 )/2022`

`<=> ( x - 1 )/2025 - 1 + ( x - 2)/2024 - 1 = ( x - 3 )/2023 - 1 + ( x- 4 )/2022 - 1`

`<=> ( x - 2026 )/2025 + ( x - 2026 )/2024 = ( x - 2026 )/2023 + ( x - 2026 )/2022`

`<=> ( x - 2026 )( 1/2025 + 1/2024 - 1/2023 - 1/2022 ) = 0`

Vì  `1/2025 + 1/2024 - 1/2023 - 1/2022` khác ` 0`

`=> x = 2026` ( `x in N` )

` Vậy  x = 2026`

`b)`$\left(x-7\right)^{x+1}-\left(x-7\right)^{x+11}=0$

$\Rightarrow\left(x-7\right)^{x+1}\left[1-\left(x-7\right)^{10}\right]=0$

$\Leftrightarrow{\begin{cases}\left(x-7\right)^{x-1}=0\\1-\left(x-7\right)^{10}=0\end{cases}}$

$\Leftrightarrow{\begin{cases}x-7=0\\\left(x-7\right)^{10}=1\end{cases}}$

$\Leftrightarrow{\begin{cases}x=7\\\left(x-7\right)^{10}=\left(\pm1\right)^{10}\end{cases}}$

$\Leftrightarrow{\begin{cases}x=7\\x-7=1\\x-7=-1\end{cases}}$

$\Leftrightarrow{\begin{cases}x=7\\x=8\\x=6\end{cases}}$