giải pt căn ( x+1) - căn (x-7) = căn (12-x)

`\sqrt{x+1} -\sqrt{x-7} =\sqrt{12-x}`

`(đk: x >= 7; x x+1-2\sqrt{(x+1)(x-7)} +x-7=12-x`

`-> x+1-2\sqrt{x^2 -7x+x-7} +x-7=12-x`

`-> 2x-6-2\sqrt{x^2 -6x-7} =12-x`

`-> -2\sqrt{x^2 -6x-7} =12-x-2x+6`

`-> -2\sqrt{x^2 -6x-7} =18-3x`

`-> 4(x^2 -6x-7)=324-108x+9x^2`

`-> 4x^2 -24x-28=324-108x+9x^2`

`-> 4x^2 -24x-28-324+108x-9x^2 =0`

`-> -5x^2 +84x-352=0`

`-> 5x^2 -84x+352=0`

`-> 5x^2 -40x-44x+352=0`

`-> 5x(x-8)-44(x-8)=0`

`-> (x-8)(5x-44)=0`

`->` $\left[\begin{matrix} x-8=0\\ 5x-44=0\end{matrix}\right.$

`->` $\left[\begin{matrix} x=8\\ x= \frac{44}{5}\end{matrix}\right.$ `(tm)`

Vậy `S={ 8; 44/5 }.`