Sửa đề: \(\sqrt{x^2-2x+1}=2024\)
=>\(\sqrt{\left(x-1\right)^2}=2024\)
=>\(\left|x-1\right|=2024\)
=>\(\left[{}\begin{matrix}x-1=2024\\x-1=-2024\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2025\\x=-2023\end{matrix}\right.\)
`sqrt{x^2 - 2x} + 1 = 2024`
ĐKXĐ: `x^2 - 2x >= 0`
`=> x(x-2) >=0`
`=>` \(\left[{}\begin{matrix}x\ge2\\x\le0\end{matrix}\right.\)
`Pt <=> sqrt{x^2 - 2x} = 2023`
`<=> x^2 - 2x = 4092529`
`<=> x^2 - 2x - 4092529 = 0`
`<=> x^2 - 2x + 1 - 4092530 = 0`
`<=> (x - 1)^2 = 4092530`
`<=> x - 1 = sqrt{4092530}` hoặc `x - 1 = - sqrt{4092530}`
`<=> x = sqrt{4092530} + 1` hoặc `x = - sqrt{4092530} + 1` (Thỏa mãn)
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