\(\left\{{}\begin{matrix}x-16=0\\3x-1=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=16\\x=\dfrac{1}{3}\end{matrix}\right.\)

\(\Leftrightarrow\left(x-16\right)\left(3x-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-16=0\\3x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=16\\x=\dfrac{1}{3}\end{matrix}\right.\)

=>x-16=0 hoặc 3x-1=0

    x     = 16         x   = ⅓

a, \(\dfrac{x^3+27}{x^2-3x+9}=\dfrac{x+3}{M}\Leftrightarrow\dfrac{\left(x+3\right)\left(x^2-3x+9\right)}{x^2-3x+9}=\dfrac{x+3}{M}\)

\(\Rightarrow M=\dfrac{x+3}{x+3}=1\)

b, \(\dfrac{M}{x+4}=\dfrac{x^2-8x+16}{16-x^2}=\dfrac{\left(x-4\right)^2}{\left(4-x\right)\left(x+4\right)}=\dfrac{4-x}{x+4}\)

\(\Rightarrow M=\dfrac{\left(4-x\right)\left(x+4\right)}{x+4}=4-x\)

c, tương tự 

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b, x <

\(\left(3x-2\right)\left(x^2+16\right)=\left(2x-7\right)\left(x^2+16\right)\)

\(\Leftrightarrow\left(3x-2\right)\left(x^2+16\right)-\left(2x-7\right)\left(x^2+16\right)=0\)

\(\Leftrightarrow\left(x^2+16\right)\left(3x-2-2x+7\right)=0\)

\(\Leftrightarrow\left(x^2+16\right)\left(x+5\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x^2+16=0\\x+5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\pm\sqrt{-16}\\x=-5\end{matrix}\right.\)

=>3x-2=2x-7

=>x=-5

\(\left(3\text{x}-2\right)\left(x^2+16\right)=\left(2\text{x}-7\right)\left(x^2+16\right)\)

\(\Leftrightarrow\left(3\text{x}-2\right)=\left(2\text{x}-7\right)\)

\(\Leftrightarrow3\text{x}-2x=-7+2\)

\(\Leftrightarrow x=-5\)

\(\dfrac{3x+2}{4}=\dfrac{16}{3x+2}\)

`=> (3x+2)^2 =4.16`

`=> (3x+2)^2 = 64`

`=> (3x+2)^2 = +- 8^2`

\(\Rightarrow\left[{}\begin{matrix}3x+2=8\\3x+2=-8\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}3x=6\\3x=-10\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=2\\x=-\dfrac{10}{3}\end{matrix}\right.\)

Bài 2: 

a: \(x^2-4x+3=0\)

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

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

a, (3x-5)^2 - (x-1)^2 = 0

(3x-5-x+1)(3x-5+x-1) =0

(2x-4)(4x-6)=0

Do đó: 2x-4=0 hoặc 4x-6=0

Th1: 2x-4=0 => 2x=4

=> x=2

Th2: 4x-6=0 => 4x=6

=> x = 4/6 =2/3

Vậy x = 2 ; 2/3

1: =>|x-4|+|x+2|=0

=>x-4=0 và x+2=0

=>\(x\in\varnothing\)

2: =>x^2-x-6=3x+5

=>x^2-4x-11=0

=>x^2-4x+4-15=0

=>(x-2)^2-15=0

=>x=căn 15+2 hoặc x=-căn 15+2

3: =>x^2-x=3x+5

=>x^2-4x-5=0

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

=>x=-1 hoặc x=5

Bài 1:

a) \(\Rightarrow3x^2+3x-2x^2-4x+x+1=0\)

\(\Rightarrow x^2=-1\left(VLý\right)\Rightarrow S=\varnothing\)

b) \(\Rightarrow\left(x-2020\right)\left(2x-1\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=2020\\x=\dfrac{1}{2}\end{matrix}\right.\)

c) \(\Rightarrow\left(x-10\right)\left(x+2\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=10\\x=-2\end{matrix}\right.\)

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

e) \(\Rightarrow\left(x+6\right)\left(x-7\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=-6\\x=7\end{matrix}\right.\)

f) \(\Rightarrow\left(5x-4\right)\left(5x+4\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{4}{5}\\x=-\dfrac{4}{5}\end{matrix}\right.\)

Bài 2:

a) \(\Rightarrow3x\left(x^2-4\right)=0\Rightarrow3x\left(x-2\right)\left(x+2\right)=0\)

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

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

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