* \(x^2-8x+12=0\Leftrightarrow x^2-2x-6x+12=0\)

\(\Leftrightarrow x\left(x-2\right)-6\left(x-2\right)=0\Leftrightarrow\left(x-2\right)\left(x-6\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-2=0\\x-6=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=2\\x=6\end{matrix}\right.\) vậy \(x=2;x=6\)

* \(x^2+5x-14=0\Leftrightarrow x^2-2x+7x-14=0\)

\(\Leftrightarrow x\left(x-2\right)+7\left(x-2\right)=0\Leftrightarrow\left(x+7\right)\left(x-2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x+7=0\\x-2=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=-7\\x=2\end{matrix}\right.\) vậy \(x=-7;x=2\)

* \(16x^2-81=0\Leftrightarrow16\left(x^2-\dfrac{81}{16}\right)=0\Leftrightarrow x^2-\dfrac{81}{16}=0\)

\(\Leftrightarrow x^2=\dfrac{81}{16}\) \(\Leftrightarrow\left[{}\begin{matrix}x=\sqrt{\dfrac{81}{16}}\\x=-\sqrt{\dfrac{81}{16}}\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{9}{4}\\x=\dfrac{-9}{4}\end{matrix}\right.\) vậy \(x=\dfrac{9}{4};x=\dfrac{-9}{4}\)

+ \(x^2-8x+12=0\)

\(\Rightarrow\left(x^2-2.4x+16\right)-4=0\)

\(\Rightarrow\left(x-4\right)^2-4=0\)

\(\Rightarrow\left(x-4\right)^2=4\)

\(\Rightarrow\left[{}\begin{matrix}x-4=2\\x-4=-2\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=6\\x=2\end{matrix}\right.\)

+ \(16x^2-81=0\)

\(\Rightarrow16x^2-9^2=0\)

\(\Rightarrow16x^2=9^2\)

\(\Rightarrow x^2=\dfrac{81}{16}\)

\(\Rightarrow\left[{}\begin{matrix}x=\sqrt{\dfrac{81}{16}}\\x=-\sqrt{\dfrac{81}{16}}\end{matrix}\right.\)

\(a,9x^2-49=0\)

\(9x^2=49\)

\(x^2=\frac{49}{9}=\frac{7^2}{3^2}=\frac{\left(-7\right)^2}{\left(-3\right)^2}\)

\(\Rightarrow\orbr{\begin{cases}x=\frac{7}{3}\\x=-\frac{7}{3}\end{cases}}\)

vậy ...

\(c,x^3-16x=0\)

\(x.\left(x^2-16\right)=0\)

\(\Rightarrow\orbr{\begin{cases}x=0\\x^2=16\end{cases}}\Rightarrow\orbr{\begin{cases}x=0\\x=4,x=-4\end{cases}}\)

vậy ...

<=>  (x² +x +4)² + 2 . 4x(x²+ x + 4) + (4x)² = 0

<=>  ( x² + x+ 4 +4x )² = 0

<=>  [(x² + x) + (4 +4x)]  =0

<=>  [x(x+1) + 4(1+x)]  =0

<=>  (x+1) + (x+4)  =0

• x+1 = 0 <=> x= -1
• x+4 = 0 <=> x= -4

*vn:vô nghiệm.

a. \(\left(x^2-2\right)\left(x^2+x+1\right)=0\)

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

\(\Leftrightarrow\left[{}\begin{matrix}\left(x-\sqrt{2}\right)\left(x+\sqrt{2}\right)=0\\\left(x+\dfrac{1}{2}\right)^2+\dfrac{3}{4}=0\left(vn\right)\end{matrix}\right.\)

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

-Vậy \(S=\left\{\pm\sqrt{2}\right\}\).

b. \(16x^2-8x+5=0\)

\(\Leftrightarrow16x^2-8x+1+4=0\)

\(\Leftrightarrow\left(4x-1\right)^2+4=0\) (vô lí)

-Vậy S=∅.

c. \(2x^3-x^2-8x+4=0\)

\(\Leftrightarrow x^2\left(2x-1\right)-4\left(2x-1\right)=0\)

\(\Leftrightarrow\left(2x-1\right)\left(x^2-4\right)=0\)

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

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=\pm2\end{matrix}\right.\)

-Vậy \(S=\left\{\dfrac{1}{2};\pm2\right\}\).

d. \(3x^3+6x^2-75x-150=0\)

\(\Leftrightarrow3x^2\left(x+2\right)-75\left(x+2\right)=0\)

\(\Leftrightarrow3\left(x+2\right)\left(x^2-25\right)=0\)

\(\Leftrightarrow3\left(x+2\right)\left(x+5\right)\left(x-5\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-2\\x=\pm5\end{matrix}\right.\)

-Vậy \(S=\left\{-2;\pm5\right\}\)

\(4+2x\left(2x+4\right)=-x\)

\(4+2x.2x+8x=-x\)

\(4x+8x+x=-4\)

\(13x=-4\)

\(x=-\frac{4}{13}\)

 Vậy pt có nghiệm là { -4/13 }

2) mình nghĩ thế này

(2x-3)^2=2x-3

Đẻ 2 cái trên = nhau thfi 

2x-3=1

=> x=2

Bài 1: 

b: \(\Leftrightarrow x-2=0\)

hay x=2

anh ơi, vậy là sai đề hả anh, chứ đề kêu chứng minh phương trình vô nghiệm mà em thấy anh ghi x=2