Tìm X biết√16x+16-√9x+9=3

$\sqrt{16x}$ `+ 26 -` $\sqrt{9x}$ `+ 9 = 3`

`<=> `$\sqrt{4^2 x}$ `+ 26 - `$\sqrt{3^2 x}$ `+ 9 = 3`

`<=>4`$\sqrt{x}$` +26 - 3`$\sqrt{x}$ `+ 9 =3`

`<=> 4`$\sqrt{x}$ `- 3`$\sqrt{x}$  `= 3 - 9 - 26`

`<=>` $\sqrt{x}$` = -32`

`<=>` `x =` $\sqrt{-32}$ `(vô lý)`

Vạy phương trình trên vô nghiệm

Answer

`\sqrt{16x + 16} - \sqrt{9x + 9} = 3` `(Đk : x \ne -1)`

`=> \sqrt{16 . (x + 1)} - \sqrt{9 . (x + 1)} = 3`

`=> 4\sqrt{x + 1} - 3\sqrt{x + 1} = 3`

`=> (4 - 3) . \sqrt{x + 1}= 3`

`=> 1 . \sqrt{x + 1} = 3`

`=> \sqrt{x + 1} = 3`

`=> x + 1 = 3^2`

`=> x + 1 = 9`

`=> x = 9 - 1`

`=> x = 8`

Vậy `S = {8}`