Giải phương trình: a, √9x + 9 + √x + 1 = 20 b, √x - 8 = √2x - 3

a) `\sqrt{9x+9}+\sqrt{x+1}=20` `(x>=-1)`

⇔`\sqrt{9(x+1)}+\sqrt{x+1}=20`

⇔`3\sqrt{x+1}+\sqrt{x+1}=20`

⇔`4\sqrt{x+1}=20`

⇔`\sqrt{x+1}=5`

⇔`x+1=25`

⇔`x=24` `(tm)`

Vậy `S={24}`

b) `\sqrt{x-8}=\sqrt{2x-3}` `(x>=8)`

⇔`x-8=2x-3`

⇔`x-2x=-3+8`

⇔`-x=5`

⇔`x=-5` `(loại)`

Vậy `S=∅`

`a)`$\text{ĐKXĐ : x≥ -1}$ 

$\sqrt{9x+9}$ `+` $\sqrt{x+1}$ `=` `20`

`⇔` `3`$\sqrt{x+1}$ `+` `(\sqrt{x+1})` `=` `20`

`⇔` `4` $\sqrt{x+1}$ `=` `20`

`⇔` $\sqrt{x+1}$ `=` `5`

`⇔` `(\sqrt{x+1})^2` `=` `5^2`

`⇔` `x` `+` `1` `=` `25`

`⇔` `x` `=` `24` `(TM)`

$\text{Vậy .... }$

`b)`$\text{ĐKXĐ : x≥ 8 }$

`\sqrt{x-8}` `=` `\sqrt{2x-3}`

`⇔` `(\sqrt{x-8})^2` `=` `(\sqrt{2x-3})^2`

`⇔` `x` `-` `8` `=` `2x` `-` `3`

`⇔` `x` `-` `2x` `=` `8` `-` `3`

`⇔` `-x` `=` `5` 

`⇔` `x` `=` `-5` `(L)`

 $\text{Vậy .... }$