Question

tìm x: \(\sqrt{x-2\sqrt{x-1}}=5\)

Answer 1

\(\Leftrightarrow\left|\sqrt{x-1}-1\right|=5\)

\(\Leftrightarrow\sqrt{x-1}-1=5\)

=>x-1=36

hay x=37

Answer 2

`\sqrt{x-2\sqrt{x-1}}=5`      `ĐK: x >= 1`

`<=>\sqrt{x-1-2\sqrt{x-1}+1}=5`

`<=>\sqrt{(\sqrt{x-1})^2-2\sqrt{x-1}+1}=5`

`<=>\sqrt{(\sqrt{x-1}-1)^2}=5`

`<=>|\sqrt{x-1}-1|=5`

`@TH1:\sqrt{x-1}-1=5`

    `<=>\sqrt{x-1}=6`

    `<=>x-1=36`

    `<=>x=37` (t/m)

`@TH2:\sqrt{x-1}-1=-5`

      `<=>\sqrt{x-1}=-4` (Vô lí)

Vậy `S={37}`