`3x-7\sqrt{x-1}=9`
`<=>-7\sqrt{x-1}=-3x+9`
`<=>-7\sqrt{x-1}=-(3x-9)`
`<=>7\sqrt{x-1}=3x-9` Điều kiện: `x\geq3`
`<=>(7\sqrt{x-1})^2=(3x-9)^2`
`<=>49(x-1)=9x^2-54x+81`
`<=>49x-49=9x^2-54x+81`
`<=>9x^2-54x+81-49x+49=0`
`<=>9x^2-103x+130=0`
`<=>9x^2-13x-90x+130=0`
`<=>x(9x-13)-10(9x-13)=0`
`<=>(9x-13)(x-10)=0`
`<=>` \(\left[ \begin{array}{l}9x-13=0\\x-10=0\end{array} \right.\)`<=>` \(\left[ \begin{array}{l}x=\dfrac{13}{9}\quad(\text{loại})\\x=10\quad(\text{nhận})\end{array} \right.\)
Vậy `x=10`
