Đặt `P=A:B`. Tìm các giá trị của `x` để `2P =` 2$\sqrt[]{x}$ +1

`ĐKXĐ: x >=0`

`P= A:B`

`=(sqrtx -1)/(sqrtx +2) : (sqrtx -2)/(sqrtx +2)`

`=(sqrtx -1)/(sqrtx +2) . (sqrtx +2)/(sqrtx -2)`

`=(sqrtx -1)/(sqrtx -2)`

Ta có:

`2P = 2sqrtx +1`

`<=>2. (sqrtx -1)/(sqrtx -2)=2sqrtx +1`

`<=>2sqrtx-2 =(2sqrtx+1)(sqrtx -2) ( x >= 0 ; x ne 4)`

`<=>2sqrtx -2=2x+sqrtx -4sqrtx -2`

`<=>2x-3sqrtx -2 -2sqrtx +2=0`

`<=>2x-5sqrtx=0`

`<=>sqrtx(2sqrtx -5)=0`

`<=>`\(\left[ \begin{array}{l}\sqrt{x}=0\\2\sqrt{x}-5=0\end{array} \right.\) 

`<=>`\(\left[ \begin{array}{l}x=0\\\sqrt{x}==\dfrac{5}{2}\end{array} \right.\) 

`<=>`\(\left[ \begin{array}{l}x=0(tm)\\x=\dfrac{25}{4}(tm)\end{array} \right.\) 

Vậy `x in {0 ; 25/4}`