`x-2\sqrt{x-1}=9`
`<=>-2\sqrt{x-1}=9-x`
`<=>-2\sqrt{x-1}=-(x-9)`
`<=>2\sqrt{x-1}=x-9` Điều kiện: `x\geq9`
`<=>(2\sqrt{x-1})^2=(x-9)^2`
`<=>4(x-1)=x^2-18x+81`
`<=>4x-4=x^2-18x+81`
`<=>x^2-18x+81-4x+4=0`
`<=>x^2-22x+85=0`
`<=>x^2-5x-17x+85=0`
`<=>x(x-5)-17(x-5)=0`
`<=>(x-17)(x-5)=0`
`<=>` \(\left[ \begin{array}{l}x-17=0\\x-5=0\end{array} \right.\)`<=>` \(\left[ \begin{array}{l}x=17\quad(\text{nhận})\\x=5\quad(\text{loại})\end{array} \right.\)
Vậy `x=17`
