TÍNH `\sqrt{25x-75} + 5/2\sqrt{4x-12} - 9\sqrt{x-3/9} = 14` `\sqrt{16x+16} - \sqrt{x-1} -7/3\sqrt{9x+9}=-2` `\sqrt{4x^2+8}-5\sqrt{{x^2+2}/25}=3`

Đáp án+Giải thích các bước giải:

 `a)`

`\sqrt{25x-75}+5/2.\sqrt{4x-12}-9\sqrt{\frac{x-3}{9}}=14` `(đk:x\ge3)`

`<=>\sqrt{25.(x-3)}+5/2.\sqrt{4.(x-3)}-9.\frac{\sqrt{x-3}}{\sqrt{9}}=14`

`<=>5\sqrt{x-3}+5/2. 2.\sqrt{x-3}-\frac{9.\sqrt{x-3}}{3}=14`

`<=>5\sqrt{x-3}+5\sqrt{x-3}-3\sqrt{x-3}=14`

`<=>7\sqrt{x-3}=14`

`<=>\sqrt{x-3}=2`

`<=>(\sqrt{x-3})^{2}=2^{2}`

`<=>x-3=4`

`<=>x=7(tmđk)`

Vậy `S={7}`

`b)`

`\sqrt{16x+16}-\sqrt{x+1}-7/3.\sqrt{9x+9}=-2` `(đk:x\ge-1)`

`<=>\sqrt{16.(x+1)}-\sqrt{x+1}-7/3. \sqrt{9.(x+1)}=-2`

`<=>4\sqrt{x+1}-\sqrt{x+1}-7/3. 3\sqrt{x+1}=-2`

`<=>3\sqrt{x+1}-7\sqrt{x+1}=-2`

`<=>-4\sqrt{x+1}=-2`

`<=>\sqrt{x+1}=2/4`

`<=>\sqrt{x+1}=1/2`

`<=>(\sqrt{x+1})^{2}=(1/2)^{2}`

`<=>x+1=1/4`

`<=>x=1/4-1`

`<=>x=1/4-4/4`

`<=>x=-3/4(tmđk)`

Vậy `S={-3/4}`

`c)`

`\sqrt{4x^{2}+8}-5.\sqrt{\frac{x^{2}+2}{25}}=3` `(đk:x\inRR)`

`<=>\sqrt{4.(x^{2}+2)}-5.\frac{\sqrt{x^{2}+2}}{\sqrt{25}}=3`

`<=>2\sqrt{x^{2}+2}-\frac{5.\sqrt{x^{2}+2}}{5}=3`

`<=>2\sqrt{x^{2}+2}-\sqrt{x^{2}+2}=3`

`<=>\sqrt{x^{2}+2}=3`

`<=>(\sqrt{x^{2}+2})^{2}=3^{2}`

`<=>x^{2}+2=9`

`<=>x^{2}=7`

`<=>x^{2}=(\pm\sqrt{7})^{2}`

`<=>x=\sqrt{7}` hoặc `x=-\sqrt{7}`

Vậy `S={\sqrt{7};-\sqrt{7}}`