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AH
Akai Haruma
Giáo viên
18 tháng 12 2023

Lời giải:
$x^2+x-12=0$

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

$\Leftrightarrow x(x-3)+4(x-3)=0$

$\Leftrightarrow (x-3)(x+4)=0$

$\Leftrightarrow x-3=0$ hoặc $x+4=0$

$\Leftrightarrow x=3$ hoặc $x=-4$

 

11 tháng 9 2017

a)  \(x^3\)\(-\)\(\frac{1}{4}x\)\(=\)\(0\)

\(x\left(x^2-\frac{1}{4}\right)=0\)

\(\Leftrightarrow\)\(\orbr{\begin{cases}x=0\\x^2-\frac{1}{4}=0\end{cases}}\)\(\Leftrightarrow\)\(\orbr{\begin{cases}x=0\\x^2=0,5^2\end{cases}}\)\(\Leftrightarrow\)\(\orbr{\begin{cases}x=0\\x=+-0,5\end{cases}}\)

Vậy .............................

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

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

\(\left(3x+2\right)\left(x-4\right)=0\)

\(\Leftrightarrow\)\(\orbr{\begin{cases}3x+2=0\\x-4=0\end{cases}}\)\(\Leftrightarrow\)\(\orbr{\begin{cases}3x=-2\\x=4\end{cases}}\)\(\orbr{\begin{cases}x=\frac{-2}{3}\\x=4\end{cases}}\)

Vậy ................................

c)  \(x^2\)\(\left(x-3\right)\)\(+\)\(12\)\(-\)\(4x\)\(=\)\(0\)

\(x^2\)\(\left(x-3\right)\)\(-\)\(4\)\(\left(x-3\right)\)\(=\)\(0\)

\(\left(x^2-4\right)\left(x-3\right)\)

\(\Leftrightarrow\)\(\orbr{\begin{cases}x^2\\x-3=0\end{cases}-4=0}\)\(\Leftrightarrow\)\(\orbr{\begin{cases}x^2\\x=3\end{cases}=2^2}\)\(\Leftrightarrow\)\(\orbr{\begin{cases}x=+-2\\x=3\end{cases}}\)

a)\(x^3-\frac{1}{4}x=0\)

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

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

\(\Leftrightarrow\hept{\begin{cases}x=0\\x-\frac{1}{2}=0\\x+\frac{1}{2}=0\end{cases}\Leftrightarrow\hept{\begin{cases}x=0\\x=\frac{1}{2}\\x=-\frac{1}{2}\end{cases}}}\)

19 tháng 10 2021

\(x^3-8-\left(x-2\right)\left(x-12\right)=0\)

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

\(\Leftrightarrow x-2=0\)

hay x=2

19 tháng 10 2021

\(\Leftrightarrow\left(x-2\right)\left(x^2+2x+4\right)-\left(x-2\right)\left(x-12\right)=0\\ \Leftrightarrow\left(x-2\right)\left(x^2+2x+4-x+12\right)=0\\ \Leftrightarrow\left(x-2\right)\left(x^2+x+16\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=2\\\left(x+\dfrac{1}{2}\right)^2+\dfrac{63}{4}=0\left(vô.lí\right)\end{matrix}\right.\\ \Leftrightarrow x=2\)

13 tháng 9 2021

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

13 tháng 9 2021

x.( x - 4)-(x2- 12) = 0

=> x2 - 4x -x2+12=0

=> -4x +12 = 0

=> -4x = -12

=> x=3

hoctot

29 tháng 11 2023

a: \(x^3-4x^2-x+4=0\)

=>\(\left(x^3-4x^2\right)-\left(x-4\right)=0\)

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

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

=>\(\left[{}\begin{matrix}x-4=0\\x^2-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4\\x^2=1\end{matrix}\right.\Leftrightarrow x\in\left\{2;1;-1\right\}\)

b: Sửa đề: \(x^3+3x^2+3x+1=0\)

=>\(x^3+3\cdot x^2\cdot1+3\cdot x\cdot1^2+1^3=0\)

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

=>x+1=0

=>x=-1

c: \(x^3+3x^2-4x-12=0\)

=>\(\left(x^3+3x^2\right)-\left(4x+12\right)=0\)

=>\(x^2\cdot\left(x+3\right)-4\left(x+3\right)=0\)

=>\(\left(x+3\right)\left(x^2-4\right)=0\)

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

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

d: \(\left(x-2\right)^2-4x+8=0\)

=>\(\left(x-2\right)^2-\left(4x-8\right)=0\)

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

=>\(\left(x-2\right)\left(x-2-4\right)=0\)

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

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

 

25 tháng 10 2020

x3 - 8 - (x - 2).(x - 12) = 0

<=> x3 - 23 - (x - 2).(x - 12) = 0

<=> (x - 2).(x2 + 2x + 4) - (x - 2).(x - 12) = 0

<=> (x - 2).(x2 + 2x + 4 - x + 12) = 0

<=> (x - 2).(x2 + x + 16) = 0

<=> x - 2 = 0

<=> x = 2

Vậy: x = 2

25 tháng 10 2020

x3 - 8 - ( x - 2 )( x - 12 ) = 0

⇔ ( x - 2 )( x2 + 2x + 4 ) - ( x - 2 )( x - 12 ) = 0

⇔ ( x - 2 )( x2 + 2x + 4 - x + 12 ) = 0

⇔ ( x - 2 )( x2 + x + 16 ) = 0

⇔ x - 2 = 0 hoặc x2 + x + 16 = 0

⇔ x = 2 < do x2 + x + 16 = ( x2 + x + 1/4 ) + 63/4 = ( x + 1/2 )2 + 63/4 ≥ 63/4 > 0 ∀ x >

NV
14 tháng 8 2021

\(\left(x-2\right)^3+6\left(x+1\right)^2-x^3+12=0\)

\(\Leftrightarrow x^3-6x^2+12x-8+6x^2+12x+6-x^3+12=0\)

\(\Leftrightarrow24x+10=0\)

\(\Leftrightarrow x=-\dfrac{5}{12}\)

13 tháng 12 2023

a: \(3\left(x-3\right)-6x=0\)

=>\(3x-9-6x=0\)

=>-3x-9=0

=>3x+9=0

=>3x=-9

=>\(x=-\dfrac{9}{3}=-3\)

b: Đề thiếu vế phải rồi bạn

c: \(2\left(x-3\right)+3x=9\)

=>2x-6+3x=9

=>5x-6=9

=>5x=6+9=15

=>x=15/5=3

d: \(x\left(x-11\right)+2\left(x-11\right)=0\)

=>\(\left(x-11\right)\left(x+2\right)=0\)

=>\(\left[{}\begin{matrix}x-11=0\\x+2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=11\\x=-2\end{matrix}\right.\)

e: \(x\left(x+2\right)+8=x^2\)

=>\(x^2+2x+8=x^2\)

=>2x+8=0

=>2x=-8

=>x=-8/2=-4

f: \(8\left(x+1\right)+2x=-2\)

=>\(8x+8+2x=-2\)

=>10x=-2-8=-10

=>\(x=-\dfrac{10}{10}=-1\)

g: 12-3(x+2)=0

=>3(x+2)=12

=>x+2=12/3=4

=>x=4-2=2

31 tháng 10 2020

a) x2 - 25x = 0

=> x(x - 25) = 0

=> \(\orbr{\begin{cases}x=0\\x=25\end{cases}}\)

b) (x - 3)2 - 36x2 = 0

=> (x - 3)2 - (6x)2 = 0

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

=> \(\orbr{\begin{cases}7x-3=0\\-5x-3=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{3}{7}\\x=-\frac{3}{5}\end{cases}}\)

c) 2x(3 - x) + 2x2 = 12

=> 6x - 2x2 + 2x2 = 12

=> 6x = 12

=> x = 2

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

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

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

=> \(\orbr{\begin{cases}x=1\\x=2\end{cases}}\)

31 tháng 10 2020

a. x - 25x = 0

\(\Leftrightarrow x\left(x-25\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x=0\\x-25=0\end{cases}}\)

\(\orbr{\begin{cases}x=0\\x=25\end{cases}}\)

Vậy ...

b.(x-3)2 - 36x= 0

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

\(\Leftrightarrow\orbr{\begin{cases}-5x-3=0\\7x-3=0\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=\frac{-3}{5}\\x=\frac{3}{7}\end{cases}}\)

Vậy...

c.2x(3-x)+2x2 = 12 

<=> 6x - 2x2 + 2x= 12

<=> 6x = 12

<=> x = 2

d. x (x-2) - x + 2 =0

<=> x(x-2 ) - (x - 2 ) = 0

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

\(\Leftrightarrow\orbr{\begin{cases}x-2=0\\x-1=0\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=2\\x=1\end{cases}}\)

Vậy...