a) \(7x\left(x+1\right)-3\left(x+1\right)=0\Rightarrow\left(x+1\right)\left(7x-3\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x+1=0\\7x+3=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-1\\x=-\dfrac{3}{7}\end{matrix}\right.\)

b) 3(x + 8) - x² - 8x = 0

=> 3(x + 8) - (x² + 8x) = 0

=> 3(x + 8) - x(x + 8) = 0

=> (x + 8)(3 - x) = 0 => \(\left[{}\begin{matrix}x+8=0\\3-x=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-8\\x=3\end{matrix}\right.\)

c) \(x^2-10x=-25\Rightarrow x^2-10x+25=0\Rightarrow\left(x-5\right)^2=0\Rightarrow x=5\)

d) Giống câu c

⇒[x+1=07x+3=0⇒⎡⎣x=−1x=−37⇒[x+1=07x+3=0⇒[x=−1x=−37

b) 3(x + 8) - x² - 8x = 0

=> 3(x + 8) - (x² + 8x) = 0

=> 3(x + 8) - x(x + 8) = 0

=> (x + 8)(3 - x) = 0 => [x+8=03−x=0⇒[x=−8x=3[x+8=03−x=0⇒[x=−8x=3

c) ${}^{}-10x=-25\Rightarrow {}^{}-10x+$

a) \(\left(x-2018\right)\cdot3=0\)

\(\Leftrightarrow x-2018=0\)

\(\Leftrightarrow x=2018\)

b) \(25\left(x-8\right)=0\)

\(\Leftrightarrow x-8=0\)

\(\Leftrightarrow x=8\)

c) \(25+\left(15+x\right)=75\)

\(\Leftrightarrow15+x=50\)

\(\Leftrightarrow x=35\)

a) x=2018

b)x=8

c)x=35

Bài 2:

a, (x-2018).3=0

<=> x-2018=0

<=>x=0+2018

<=>x=2018

Vậy x=2018

b, 25(x-8)=0

<=> x-8=0

<=> x=0+8

<=>x=8

Vậy x=8

c, 25+(15+x)=75

<=> 25+15+x=75

<=> 40+x=75

<=>x=75-40

<=>x=35

Vậy x=35

b) x(x-4) - 2x+8 = 0
    x(x-4) - 2(x-4) = 0
    (x-2) (x-4) = 0
TH1: x-2=0              TH2: x-4=0
            x=2                          x=4
Vậy x\(\in\){2;4}

\(b,\Leftrightarrow\left(x-4\right)\left(x-2\right)=0\Leftrightarrow\left[{}\begin{matrix}x=2\\x=4\end{matrix}\right.\\ c,\Leftrightarrow\left(x-5\right)\left(x+5\right)-\left(x+5\right)=0\\ \Leftrightarrow\left(x+5\right)\left(x-6\right)=0\Leftrightarrow\left[{}\begin{matrix}x=6\\x=-5\end{matrix}\right.\\ d,\Leftrightarrow\left(2x-1\right)^2-\left(2x-1\right)\left(2x+1\right)=0\\ \Leftrightarrow\left(2x-1\right)\left(2x-1-2x-1\right)=0\\ \Leftrightarrow x=\dfrac{1}{2}\\ e,\Leftrightarrow\left(3x-1-x-5\right)\left(3x-1+x+5\right)=0\\ \Leftrightarrow\left(2x-6\right)\left(4x+4\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=-1\\x=3\end{matrix}\right.\\ f,\Leftrightarrow\left(x-2\right)\left(x^2+2x+4\right)-\left(x-2\right)\left(x-12\right)=0\\ \Leftrightarrow\left(x-2\right)\left(x^2+x+16\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=2\\\left(x+\dfrac{1}{2}\right)^2+\dfrac{63}{4}=0\left(vô.n_0\right)\end{matrix}\right.\\ \Leftrightarrow x=2\)

b) x(x-4)-2x+8=0

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

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

th1: x-4=0

x=4

th2: x-2=0

x=2

Vậy x thuộc tập hợp 4;-2

\(\left(x-2\right)\left(4x-20\right)=0\\ \Rightarrow\left[{}\begin{matrix}x-2=0\\4x-20=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=2\\4x=20\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=2\\x=5\end{matrix}\right.\\ \left(x-5\right)\left(25-5x?\right)=0\\ \Rightarrow\left[{}\begin{matrix}x-5=0\\25-5x=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=5\\5x=25\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=5\\x=5\end{matrix}\right.\\ \left(x-4\right)\left(2x-8\right)\\ \Rightarrow\left[{}\begin{matrix}x-4=0\\2x-8=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=4\\2x=8\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=4\\x=4\end{matrix}\right.\)

a,(x-2)(4x-20)=0

=>x-2=0 hoặc 4x-20=0

=>x=2 hoặc x=5

b,(x-5)(25-5)=0

=>x-5=0  ( vì 25-5 ≠0)

=>x=5

c,(x-4)(2x-8)=0

=>x-4=0 hoặc 2x-8=0

=>x=4 

\(\left(x-2\right)\left(4x-20\right)=0\\ \Rightarrow\left[{}\begin{matrix}x-2=0\\4x-20=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=2\\4x=20\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=2\\x=5\end{matrix}\right.\)

Vậy x={2;5}

________________________

\(\left(x-5\right)\left(25-5\right)=0\\ \Rightarrow\left(x-5\right)20=0\\ \Rightarrow x-5=0\\ \Rightarrow x=5\)

Vậy x=5

_____________________

\(\left(x-4\right)\left(2x-8\right)=0\\ \Rightarrow2x-8=x-4\\ \Rightarrow2x-8-x=-4\\ \Rightarrow x-8=-4\\ \Rightarrow x=-4+8\\ \Rightarrow x=4\)

\(a,96-3\left(x+8\right)=42\\ \Rightarrow3\left(x+8\right)=54\\ \Rightarrow x+8=18\\ \Rightarrow x=10.\\ b,15.5\left(x-25\right)-225=0\\ \Rightarrow75\left(x-25\right)-225=0\\ \Rightarrow75\left(x-25\right)=225\\ \Rightarrow x-25=3\\ \Rightarrow x=28.\\ c,250:x+15=25\\ \Rightarrow250:x=10\\ \Rightarrow x=25\\ d,36:\left(x-5\right)=2^2\\ \Rightarrow36:\left(x-5\right)=4\\ \Rightarrow x-5=9\\ \Rightarrow x=14.\\ e,\left[3.\left(70-x\right)+5\right]:2=46\\ \Rightarrow3.\left(70-x\right)+5=92\\ \Rightarrow3\left(70-x\right)=87\\ \Rightarrow70-x=29\\ \Rightarrow x=41.\)

\(a,\left(-31\right).\left(x+7\right)=0\\ \Rightarrow x+7=0\\ \Rightarrow x=-7\\ b,\left(8-x\right).\left(x+13\right)=0\\ \Rightarrow\left[{}\begin{matrix}8-x=0\\x+13=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=8\\x=-13\end{matrix}\right.\\ c,\left(x^2-25\right)\left(3-x\right)=0\\ \Rightarrow\left(x-5\right)\left(x+5\right)\left(3-x\right)=0\\\Rightarrow \left[{}\begin{matrix}x-5=0\\x+5=0\\3-x=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=5\\x=-5\\x=3\end{matrix}\right.\\ d,\left(x-3\right)\left(x^2+4\right)=0\\ \Rightarrow\left[{}\begin{matrix}x-3=0\\x^2+4=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=3\\x^2=-4\left(loại\right)\end{matrix}\right.\\ \Rightarrow x=3\)

a, (–31) . (x +7)=0

<=>  x +7 = 0

<=> x = -7

Vậy x \(\in\left\{-7\right\}\)

b, (8 – x) . (x + 13) = 0

<=> \(\left[{}\begin{matrix}8-x=0\\x+13=0\end{matrix}\right.\)   <=> \(\left[{}\begin{matrix}x=8\\x=-13\end{matrix}\right.\)

Vậy x \(\in\left\{8;-13\right\}\)

c,(x²– 25) . (3– x )=0

<=> (x - 5) (x + 5) (3 - x) = 0

<=> \(\left[{}\begin{matrix}x-5=0\\x+5=0\\3-x=0\end{matrix}\right.\)   <=> \(\left[{}\begin{matrix}x=5\\x=-5\\x=3\end{matrix}\right.\)

Vậy x \(\in\left\{5;-5;3\right\}\)

d, ( x - 3 ) (x² + 4) = 0

<=> \(\left[{}\begin{matrix}x-3=0\\x^2+4=0\end{matrix}\right.\)   <=> \(\left[{}\begin{matrix}x=3\\x^2=-4\end{matrix}\right.\)_{(vô lý)}

Vậy x \(\in\left\{3\right\}\)

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