\(a,3x-12=0\)

\(\Leftrightarrow3x=12\)

\(\Leftrightarrow x=4\)

\(b,\left(x-2\right)\left(2x+3\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-2=0\\2x+3=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-\dfrac{3}{2}\end{matrix}\right.\)

\(c,\dfrac{x+2}{x-2}-\dfrac{6}{x+2}=\dfrac{x^2}{x^2-4}\left(dkxd:x\ne\pm2\right)\)

\(\Leftrightarrow\dfrac{\left(x+2\right)^2-6\left(x-2\right)-x^2}{x^2-4}=0\)

\(\Leftrightarrow x^2+4x+4-6x+12-x^2=0\)

\(\Leftrightarrow-2x+16=0\)

\(\Leftrightarrow-2x=-16\)

\(\Leftrightarrow x=8\left(tmdk\right)\)

\(a,3x-12=0\)

\(\Leftrightarrow3x=12\)

\(\Leftrightarrow x=4.\)

Vậy \(S=\left\{4\right\}\)

\(b,\left(x-2\right)\left(2x+3\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x-2=0\\2x+3=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=2.\\x=\dfrac{-3}{2}.\end{matrix}\right.\)

Vậy \(S=\left\{2;\dfrac{-3}{2}\right\}\)

\(c,\dfrac{x+2}{x-2}-\dfrac{6}{x+2}=\dfrac{x^2}{x^2-4}\left(ĐKXĐ:x\ne\pm2\right)\)

\(\Leftrightarrow\dfrac{\left(x+2\right)^2}{\left(x-2\right)\left(x+2\right)}-\dfrac{6\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}-\dfrac{x^2}{\left(x-2\right)\left(x+2\right)}=0\)

\(\Leftrightarrow\dfrac{x^2+4x+4}{\left(x-2\right)\left(x+2\right)}-\dfrac{6x-12}{\left(x-2\right)\left(x+2\right)}-\dfrac{x^2}{\left(x-2\right)\left(x+2\right)}=0\)

\(\Rightarrow x^2+4x+4-6x+12-x^2=0\)

\(\Leftrightarrow-2x+16=0\)

\(\Leftrightarrow-2x=-16\)

\(\Leftrightarrow x=8\left(tm\right).\)

Vậy \(S=\left\{8\right\}\)

Giải như sau.

(1)+(2)⇔x2−2x+1+√x2−2x+5=y2+√y2+4⇔(x2−2x+5)+√x2−2x+5=y2+4+√y2+4⇔√y2+4=√x2−2x+5⇒x=3y(1)+(2)⇔x2−2x+1+x2−2x+5=y2+y2+4⇔(x2−2x+5)+x2−2x+5=y2+4+y2+4⇔y2+4=x2−2x+5⇒x=3y

⇔√y2+4=√x2−2x+5⇔y2+4=x2−2x+5, chỗ này do hàm số f(x)=t2+tf(x)=t2+t đồng biến ∀t≥0∀t≥0
Công việc còn lại là của bạn ! 

\(\left(x+6\right)\left(2x+1\right)=0\)

<=>  \(\orbr{\begin{cases}x+6=0\\2x+1=0\end{cases}}\)

<=>  \(\orbr{\begin{cases}x=-6\\x=-\frac{1}{2}\end{cases}}\)

Vậy....

hk tốt

^^

a: =>(x^2-1)(x^2-4)=0

=>(x-1)(x+1)(x-2)(x+2)=0

=>\(x\in\left\{1;-1;2;-2\right\}\)

b: =>2x^4-4x^2+x^2-2=0

=>(x^2-2)(2x^2+1)=0

=>x^2-2=0

=>\(x=\pm\sqrt{2}\)

c: =>(căn x-6)(căn x+1)=0

=>căn x-6=0

=>x=36

a. \(\Leftrightarrow\left(2x-5\right)\left(2x+5\right)\left(x+1\right)\left(2x-9\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}2x-5=0\\2x+5=0\\x+1=0\\2x-9=0\end{matrix}\right.\) \(\Rightarrow x=\)

b. \(\Leftrightarrow x^3+x+3x^2+3=0\)

\(\Leftrightarrow x\left(x^2+1\right)+3\left(x^2+1\right)=0\)

\(\Leftrightarrow\left(x+3\right)\left(x^2+1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x+3=0\\x^2+1=0\left(vn\right)\end{matrix}\right.\)

c. \(\Leftrightarrow2x\left(3x-1\right)^2-\left(9x^2-1\right)=0\)

\(\Leftrightarrow\left(6x^2-2x\right)\left(3x-1\right)-\left(3x-1\right)\left(3x+1\right)=0\)

\(\Leftrightarrow\left(3x-1\right)\left(6x^2-5x-1\right)=0\)

\(\Leftrightarrow\left(3x-1\right)\left(x-1\right)\left(6x+1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}3x-1=0\\x-1=0\\6x+1=0\end{matrix}\right.\)

d.

\(\Leftrightarrow x^3-3x^2+2x-3x^2+9x-6=0\)

\(\Leftrightarrow x\left(x^2-3x+2\right)-3\left(x^2-3x+2\right)=0\)

\(\Leftrightarrow\left(x-3\right)\left(x^2-3x+2\right)=0\)

\(\Leftrightarrow\left(x-3\right)\left(x-1\right)\left(x-2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\x-1=0\\x-2=0\end{matrix}\right.\)

e.

\(\Leftrightarrow x^3+2x^2+x+3x^2+6x+3=0\)

\(\Leftrightarrow x\left(x^2+2x+1\right)+3\left(x^2+2x+1\right)=0\)

\(\Leftrightarrow\left(x+3\right)\left(x^2+2x+1\right)=0\)

\(\Leftrightarrow\left(x+3\right)\left(x+1\right)^2=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x+3=0\\x+1=0\end{matrix}\right.\)

Bài 1)1)\(x^2+5x+6=x^2+3x+2x+6\)=0

=x(x+3)+2(x+3)=(x+2)(x+3)=0

Dễ rồi

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

=x(x-3)+2(x-3)=0

=(x+2)(x-3)=0

Dễ rồi

3)Phương trình tương đương:\(\left(x^2+1\right)\left(x+2\right)^2=0\)

Vì \(x^2+1>0\)

=>\(\left(x+2\right)^2=0\)

Dễ rồi

4)Phương trình tương đương\(x^2\left(x+1\right)+\left(x+1\right)\)=0

=> \(\left(x^2+1\right)\left(x+1\right)=0Vì\) \(x^2+1>0\)

=>x+1=0

=>..................

5)\(x^2-7x+6=x^2-6x-x+6\) =0

=x(x-6)-(x-6)=0

=(x-1)(x-6)=0

=>.....

6)\(2x^2-3x-5=2x^2+2x-5x-5\)=0

=2x(x+1)-5(x+1)=0

=(2x-5)(x+1)=0

7)\(x^2-3x+4x-12\)=x(x-3)+4(x-3)=(x+4)(x-3)=0

Dễ rồi

Nghỉ đã hôm sau làm mệt

baif 4 là tìm x đấy m,n ạ

bn chờ đến 3 rưỡi nhé h mk bận

dễ mà, rảnh ỗi đăng cái đề ko đâu vào đâulên làm j, cái này dùng hằng đẳng thức cân hết được à