a.

\(x\left(x+7\right)=0\)

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

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

b.

\(\left(x+12\right)\left(x-3\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x+12=0\\x-3=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-12\\x=3\end{matrix}\right.\)

c.

\(\left(-x+5\right)\left(3-x\right)=0\)

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

\(\Leftrightarrow\left[{}\begin{matrix}x=5\\x=3\end{matrix}\right.\)

d.

Em kiểm tra lại ngoặc cuối của câu này

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

\(\Leftrightarrow x^3-9x^2+27x-27+x^3+9x^2+27x+27=0\)\(\Leftrightarrow2x^3+54x^2=0\)

\(\Leftrightarrow x^2\left(2x+54\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=0\\2x+54=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x=-27\end{matrix}\right.\)

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

\(\Leftrightarrow x^3+3x^2+3x+1-x^3+3x^2-3x+1=0\)\(\Leftrightarrow6x^2+2=0\)

\(\Leftrightarrow6x^2=-2\)

\(\Leftrightarrow x^2=-3\) ( vô lí)

Vậy pt vô nghiệm

\(c,x^2-4x+3=0\)

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

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

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

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

\(d,4x^2+4x+1=0\)

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

\(\Rightarrow2x+1=0\)

\(\Leftrightarrow2x=-1\Rightarrow x=-\dfrac{1}{2}\)

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

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

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

\(\Leftrightarrow-2x-5=0\)

\(\Leftrightarrow-2x=5\Rightarrow x=-\dfrac{5}{2}\)

Học tốt nha you <3

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

\(\Leftrightarrow x^3-9x^2+27x-27+x^3+9x^2+27x+27=0\)\(\Leftrightarrow2x^3+54x^2=0\)

\(\Leftrightarrow x^2\left(2x+54\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=0\\2x+54=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x=-27\end{matrix}\right.\)

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

\(\Leftrightarrow x^3+3x^2+3x+1-x^3+3x^2-3x+1=0\)\(\Leftrightarrow6x^2+2=0\)

\(\Leftrightarrow6x^2=-2\)

\(\Leftrightarrow x^2=-3\) ( vô lí)

Vậy pt vô nghiệm

\(c,x^2-4x+3=0\)

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

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

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

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

\(d,4x^2+4x+1=0\)

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

\(\Rightarrow2x+1=0\)

\(\Leftrightarrow2x=-1\Rightarrow x=-\dfrac{1}{2}\)

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

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

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

\(\Leftrightarrow-2x-5=0\)

\(\Leftrightarrow-2x=5\Rightarrow x=-\dfrac{5}{2}\)

Học tốt nha you <3

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

\(\Leftrightarrow x^3-9x^2+27x-27+x^3+9x^2+27x+27=0\)\(\Leftrightarrow2x^3+54x^2=0\)

\(\Leftrightarrow x^2\left(2x+54\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=0\\2x+54=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x=-27\end{matrix}\right.\)

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

\(\Leftrightarrow x^3+3x^2+3x+1-x^3+3x^2-3x+1=0\)\(\Leftrightarrow6x^2+2=0\)

\(\Leftrightarrow6x^2=-2\)

\(\Leftrightarrow x^2=-3\) ( vô lí)

Vậy pt vô nghiệm

\(c,x^2-4x+3=0\)

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

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

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

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

\(d,4x^2+4x+1=0\)

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

\(\Rightarrow2x+1=0\)

\(\Leftrightarrow2x=-1\Rightarrow x=-\dfrac{1}{2}\)

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

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

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

\(\Leftrightarrow-2x-5=0\)

\(\Leftrightarrow-2x=5\Rightarrow x=-\dfrac{5}{2}\)

Học tốt nha you <3

1) Do x ∈ Z và 0 < x < 3

⇒ x ∈ {1; 2}

2) Do x ∈ Z và 0 < x ≤ 3

⇒ x ∈ {1; 2; 3}

3) Do x ∈ Z và -1 < x ≤ 4

⇒ x ∈ {0; 1; 2; 3; 4}

đăng cho vui à

Làm theo công thức: tích bằng 0 thì một trong x thừa số bằng 0 rồi xét các trường hợp

1. x ( x + 7 ) = 0
( 1 ) x = 0
( 2 ) x + 7 = 0 => x = -7
S = { -7 ; 0 }

2. ( x + 12 ) ( x - 3 ) = 0
( 1 ) x + 12 = 0 => x = -12
( 2 ) x - 3 = 0 => x = 3
S = { -12 ; 3 }

3. ( -x + 5 ) ( 3 - x ) = 0
( 1 ) -x + 5 = 0 => -x = -5 => x = 5
( 2 ) 3 - x = 0 => x = 3
S = { 3 ; 5 }

4. x ( 2 + x ) ( 7 - x ) = 0
( 1 ) x = 0
( 2 ) 2 + x = 0 => x = -2
( 3 ) 7 - x = 0 => x = 7
S = { -2 ; 0 ; 7 }

5. ( x - 1 ) ( x + 2 ) ( -x - 3 ) = 0
( 1 ) x - 1 = 0 => x = 1
( 2 ) x + 2 = 0 => x = -2
( 3 ) -x - 3 = 0 => -x = 3 => x = -3
S = { -3 ; -2 ; 1 }

\(1,x.\left(x+7\right)=0\)

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

\(2,\left(x+12\right).\left(x-3\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x+12=0\\x-3=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=-12\\x=3\end{cases}}}\)

\(3,\left(-x+5\right).\left(3-x\right)=0\)

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

4/   \(x.\left(2+x\right).\left(7-x\right)=0\)

   \(\hept{\begin{cases}x=0\\2+x=0\\7-x=0\end{cases}}\) =>   \(\hept{\begin{cases}x=0\\x=-2\\x=7\end{cases}}\)

Vậy \(x=\left\{0,-2,7\right\}\)

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

\(\hept{\begin{cases}x-1=0\\x+2=0\\-x-3=0\end{cases}}\)=>   \(\hept{\begin{cases}x=1\\x=-2\\x=-3\end{cases}}\)

a) x=0 hoặc x+7=0

suy ra x=0 hoặc x=-7

b) x+12=0 hoặc x-3=0

x=-12 hoặc x=3

c) x=0 hoặc x+2=0 hoặc 7-x=0

x=0 hoặc x=-2 hoặc x=7

d) x-1=0 hoặc x+2=0 hoặc -x-3=0

suy ra x=1 hoặc x=-2 hoặc x=-3

Bài làm

x( x + 7 ) = 0

<=> x = 0 hoẵ x + 7 = 0

=> x = 0 hoặc x = -7

Vậy x = 0 hoặc x = -7

( x + 12 )( x - 3 ) = 0

<=> x + 12 = 0 hoặc x - 3 = 0

=> x = -12 hoặc x = 3

Vậy x = -12 hoặc x = 3

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

<=> -x + 5 = 0 hoặc 3 - x = 0

=> x = 5 hoặc x = 3

Vậy x = 5 hoặc x = 3

x( 2 + x )( 7 - x ) = 0

<=> x = 0 hoặc 2 + x = 0 hoặc 7 - x = 0

=> x = 0 hoặc x = -2 hoặc x = 7

Vậy x = 0 hoặc x = -2 hoặc x j 7

( x - 1 )( x + 2 )( -x - 3 ) = 0

<=> ( x - 1 ) = 0 hoặc x + 2 = 0 hoặc ( -x - 3 ) = 0

<=> x = 1 hoăc x = -2 hoặc x = ( -3) 

Vậy x = 1 hoặc x = 2 hoặc x = -3

x.(x+7)=0

=>x =0 hoặc x+7=0

                     x=0-7

                     x=(-7)

Vậy x thuộc {0;-7}

(x+12).(x-3)=0

=>x+12=0 hoặc x-3=0

 x=0-12              x=0+3

x=(-12)              x=3

Vậy x thuộc {-12;3}

Các câu khác bn lm tương tự nha

X=4

\(a,\left(x+5\right)\left(x-4\right)=0.\)

\(\Leftrightarrow\left[{}\begin{matrix}x+5=0.\\x-4=0.\end{matrix}\right.\)

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

Vậy..........

\(b,\left(x-1\right)\left(x-3\right)=0.\)

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

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

Vậy..........

\(c,\) Sửa đề:

\(\left(3-x\right)\left(x-3\right)=0.\)

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

\(\Leftrightarrow x=3.\)

Vậy..........

\(d,x\left(x+1\right)=0.\)

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

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

Vậy..........

(3 - \(x\)) - (\(x-3\)) = 0

3 - \(x\) - \(x\) + 3 = 0

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

     6 - 2\(x\) = 0

        2\(x\) = 6

        \(x\) = 6 : 2

        \(x\) = 3

Vậy \(x\) = 3

(x+12).(x-3)=0

=> ta có 2 trường hợp:

+) x+12 = 0 => x = 0-12=-12

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

Vậy x= 0 hoặc x = 3

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

=> Ta có 2 trường hợp:

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

+) 3 - x =0  => x=3-0=3

Vậy x= 5 hoặc 3

A) ( x+12).(x-3)=0 \(\orbr{\begin{cases}x+12=0\\x-3=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-12\in Z\\x=3\in Z\end{cases}}\)Vậy..