Lời giải:

1. ĐKXĐ: $x\geq \frac{-5+\sqrt{21}}{2}$

PT $\Leftrightarrow x^2+5x+1=x+1$

$\Leftrightarrow x^2+4x=0$

$\Leftrightarrow x(x+4)=0$

$\Rightarrow x=0$ hoặc $x=-4$

Kết hợp đkxđ suy ra $x=0$

2. ĐKXĐ: $x\leq 2$

PT $\Leftrightarrow x^2+2x+4=2-x$

$\Leftrightarrow x^2+3x+2=0$

$\Leftrightarrow (x+1)(x+2)=0$

$\Leftrightarrow x+1=0$ hoặc $x+2=0$

$\Leftrightarrow x=-1$ hoặc $x=-2$
3.

ĐKXĐ: $-2\leq x\leq 2$

PT $\Leftrightarrow \sqrt{2x+4}=\sqrt{2-x}$

$\Leftrightarrow 2x+4=2-x$

$\Leftrightarrow 3x=-2$

$\Leftrightarrow x=\frac{-2}{3}$ (tm)

a, ĐKXĐ: ...

\(\sqrt{3x^2-2x+6}+3-2x=0\)

\(\Leftrightarrow\sqrt{3x^2-2x+6}=2x-3\)

\(\Leftrightarrow3x^2-2x+6=4x^2-12x+9\)

\(\Leftrightarrow4x^2-10x+3=0\)

.....

b, ĐKXĐ: ...

\(\sqrt{x+1}+\sqrt{x-1}=4\\ \Leftrightarrow x+1+x-1+2\sqrt{\left(x+1\right)\left(x-1\right)}=16\\ \Leftrightarrow2\sqrt{x^2-1}=16-2x\\ \Leftrightarrow\sqrt{x^2-1}=8-x\\ \Leftrightarrow x^2-1=64-16x+x^2\\ \Leftrightarrow65-16x=0\\ \Leftrightarrow x=\dfrac{65}{16}\)

b) Đặt \(\sqrt{x^2-6x+6}=a\left(a\ge0\right)\)

\(\Rightarrow a^2+3-4a=0\)

=> (a - 3).(a - 1) = 0

=> \(\left[{}\begin{matrix}a=3\\a=1\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}\sqrt{x^2-6x+6}=3\\\sqrt{x^2-6x+6}=1\end{matrix}\right.\)

Bình phương lên giải tiếp nhé!

c) Tương tư câu b nhé

ĐKXĐ: \(\left\{{}\begin{matrix}x\ge\frac{7}{2}\\x=2\end{matrix}\right.\)

\(\Leftrightarrow\sqrt{x-2}\left(\sqrt{2x-7}-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x-2}=0\\\sqrt{2x-7}=1\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=2\\x=4\end{matrix}\right.\)

ĐK: `x<=-1 ; x>= 1`

`\sqrt(x^2-1)+\sqrt(x^2-2x+1)=0`

`<=> \sqrt((x-1)(x+1)) + \sqrt((x-1)^2)=0`

`<=> \sqrt(x-1) (\sqrt(x+1) + \sqrt(x-1))=0`

\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x-1}=0\\\sqrt{x+1}+\sqrt{x-1}=0\left(VN\right)\end{matrix}\right.\\ \Leftrightarrow x=1\)

Vậy `S={1}`.

ĐKXĐ : \(\left[{}\begin{matrix}x\ge1\\x\le-1\end{matrix}\right.\)

\(\sqrt{x^2-1}+\sqrt{x^2-2x+1}=0\)\(\)

\(\)\(\Leftrightarrow\left\{{}\begin{matrix}x^2-1=0\\x^2-2x+1=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x^2=1\\\left(x-1\right)^2=0\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x=\pm1\\x=1\end{matrix}\right.\)\(\)

\(\Leftrightarrow x=1\)

Vậy S = {1}

\(1)\) ĐKXĐ : \(x\ge3\)

\(\sqrt{x^2-4x+3}+\sqrt{x-1}=0\)

\(\Leftrightarrow\)\(\sqrt{\left(x^2-4x+4\right)-1}+\sqrt{x-1}=0\)

\(\Leftrightarrow\)\(\sqrt{\left(x-2\right)^2-1}+\sqrt{x-1}=0\)

\(\Leftrightarrow\)\(\sqrt{\left(x-2-1\right)\left(x-2+1\right)}+\sqrt{x-1}=0\)

\(\Leftrightarrow\)\(\sqrt{\left(x-3\right)\left(x-1\right)}+\sqrt{x-1}=0\)

\(\Leftrightarrow\)\(\sqrt{x-1}\left(\sqrt{x-3}+1\right)=0\)

\(\Leftrightarrow\)\(\orbr{\begin{cases}\sqrt{x-1}=0\\\sqrt{x-3}+1=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=1\\x\in\left\{\varnothing\right\}\end{cases}}}\)

Vậy \(x=1\)

\(2)\)\(\sqrt{x^2-2x+1}-\sqrt{x^2-6x+9}=10\)

\(\Leftrightarrow\)\(\sqrt{\left(x-1\right)^2}-\sqrt{\left(x-3\right)^2}=10\)

\(\Leftrightarrow\)\(\left|x-1\right|-\left|x-3\right|=10\)

+) Với \(\hept{\begin{cases}x-1\ge0\\x-3\ge0\end{cases}\Leftrightarrow\hept{\begin{cases}x\ge1\\x\ge3\end{cases}\Leftrightarrow}x\ge3}\) ta  có : 

\(x-1-x+3=10\)

\(\Leftrightarrow\)\(0=8\) ( loại ) 

+) Với \(\hept{\begin{cases}x-1< 0\\x-3< 0\end{cases}\Leftrightarrow\hept{\begin{cases}x< 1\\x< 3\end{cases}\Leftrightarrow}x< 1}\) ta có : 

\(1-x+x-3=10\)

\(\Leftrightarrow\)\(0=12\) ( loại ) 

Vậy không có x thỏa mãn đề bài 

Chúc bạn học tốt ~ 

PS : mới lp 8 sai đừng chửi nhé :v