1: Ta có: \(2x\left(x+3\right)-6\left(x-3\right)=0\)

\(\Leftrightarrow2x^2+6x-6x+18=0\)

\(\Leftrightarrow2x^2+18=0\left(loại\right)\)

2: Ta có: \(2x^2\left(2x+3\right)+\left(2x+3\right)=0\)

\(\Leftrightarrow2x+3=0\)

hay \(x=-\dfrac{3}{2}\)

3: Ta có: \(\left(x-2\right)\left(x+1\right)-4x\left(x-2\right)=0\)

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

\(\Leftrightarrow\left[{}\begin{matrix}x=2\\x=\dfrac{1}{3}\end{matrix}\right.\)

4: Ta có: \(2x\left(x-5\right)-3x+15=0\)

\(\Leftrightarrow\left(x-5\right)\left(2x-3\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=5\\x=\dfrac{3}{2}\end{matrix}\right.\)

5: Ta có: \(3x\left(x+4\right)-2x-8=0\)

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

\(\Leftrightarrow\left[{}\begin{matrix}x=-4\\x=\dfrac{2}{3}\end{matrix}\right.\)

6: Ta có: \(x^2\left(2x-6\right)+2x-6=0\)

\(\Leftrightarrow2x-6=0\)

hay x=3

5: =>4x^2-1/9=0

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

=>x=1/6 hoặc x=-1/6

6: =>x-1=2

=>x=3

7:=>(2x-1)^3=-27

=>2x-1=-3

=>2x=-2

=>x=-1

8: =>1/8(x-1)^3=-125

=>(x-1)^3=-1000

=>x-1=-10

=>x=-9

3: =>(5x-5)^2-4=0

=>(5x-7)(5x-3)=0

=>x=3/5 hoặc x=7/5

4: =>(5x-1)^2=0

=>5x-1=0

=>x=1/5

1: =>(3x-1)(2x-1)=0

=>x=1/3 hoặc x=1/2

2: =>x^2(2x-3)-4(2x-3)=0

=>(2x-3)(x^2-4)=0

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

=>x=3/2;x=2;x=-2

`@` `\text {Answer}`

`\downarrow`

`1,`

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

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

`<=> 2x(3x - 1) - (3x - 1) = 0`

`<=> (2x - 1)(3x-1) = 0`

`<=>`\(\left[{}\begin{matrix}2x-1=0\\3x-1=0\end{matrix}\right.\)

`<=>`\(\left[{}\begin{matrix}2x=1\\3x=1\end{matrix}\right.\)

`<=>`\(\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=\dfrac{1}{3}\end{matrix}\right.\)

Vậy,  `S = {1/2; 1/3}`

`2,`

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

`<=> x^2(2x - 3) - 8x + 12 =0`

`<=> x^2(2x - 3) - (8x - 12) = 0`

`<=> x^2(2x - 3) - 4(2x - 3) = 0`

`<=> (x^2 - 4)(2x - 3) = 0`

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

`<=>`\(\left[{}\begin{matrix}x^2=4\\2x=3\end{matrix}\right.\)

`<=>`\(\left[{}\begin{matrix}x^2=\left(\pm2\right)^2\\x=\dfrac{3}{2}\end{matrix}\right.\)

`<=>`\(\left[{}\begin{matrix}x=\pm2\\x=\dfrac{3}{2}\end{matrix}\right.\)

Vậy, `S = {+-2; 3/2}`

`3,`

\(25\left(x-1\right)^2-4=0\)

`<=> 25(x-1)(x-1) - 4 = 0`

`<=> 25(x^2 - 2x + 1) - 4 = 0`

`<=> 25x^2 - 50x + 25 - 4 = 0`

`<=> 25x^2 - 15x - 35x + 21 = 0`

`<=> (25x^2 - 15x) - (35x - 21) = 0`

`<=> 5x(5x - 3) - 7(5x - 3) = 0`

`<=> (5x - 7)(5x - 3) = 0`

`<=>`\(\left[{}\begin{matrix}5x-7=0\\5x-3=0\end{matrix}\right.\)

`<=>`\(\left[{}\begin{matrix}5x=7\\5x=3\end{matrix}\right.\)

`<=>`\(\left[{}\begin{matrix}x=\dfrac{7}{5}\\x=\dfrac{3}{5}\end{matrix}\right.\)

Vậy, `S = {7/5; 3/5}`

`4,`

\(25x^2-10x+1=0\)

`<=> 25x^2 - 5x - 5x + 1 = 0`

`<=> (25x^2 - 5x) - (5x - 1) = 0`

`<=> 5x(5x - 1) - (5x - 1) = 0`

`<=> (5x - 1)(5x-1)=0`

`<=> (5x-1)^2 = 0`

`<=> 5x - 1 = 0`

`<=> 5x = 1`

`<=> x = 1/5`

Vậy,` S = {1/5}.`

`@` `\text {Ans}`

`\downarrow`

`5,`

`-4x^2 + 1/9 = 0`

`<=> -4x^2 = 0 - 1/9`

`<=> -4x^2 = -1/9`

`<=> 4x^2 = 1/9`

`<=> x^2 = 1/9 \div 4`

`<=> x^2 = 1/36`

`<=> x^2 = (+-1/6)^2`

`<=> x = +-1/36`

Vậy, `S = {1/36; -1/36}`

`6,`

`(x-1)^3 = 8`

`<=> (x-1)^3 = 2^3`

`<=> x-1=2`

`<=> x = 2 + 1`

`<=> x = 3`

Vậy, `S = {3}`

`7,`

`(2x-1)^3 + 27 = 0`

`<=> (2x - 1)^3 = -27`

`<=> (2x-1)^3 = (-3)^3`

`<=> 2x - 1 = -3`

`<=> 2x = -3 + 1`

`<=> 2x = -2`

`<=> x = -1`

Vậy,` S = {-1}`

`8,`

`125 + 1/8(x-1)^3 = 0`

`<=> 1/8(x-1)^3 = - 125`

`<=> (x-1)^3 = -125 \div 1/8`

`<=> (x-1)^3 = -1000`

`<=> (x-1)^3 = (-10)^3`

`<=> x - 1 = - 10`

`<=> x = -10+1`

`<=> x = -9`

Vậy, `S = {-9}.`

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

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

=> x = 3 hoặc x = -2

2,(x-5)(7-x)=0

=>\(\left[{}\begin{matrix}x-5=0\\7-x=0\end{matrix}\right.\)

=> x = 5 hoặc x = 7

3.(2x + 3)(-x + 7)=0

=>\(\left[{}\begin{matrix}2x+3=0\\-x+7=0\end{matrix}\right.\)

=> x = -3/2 hoặc  x = 7.

4.(-10x + 5 )(2x-8)=0

=>\(\left[{}\begin{matrix}-10x+5=0\\2x-8=0\end{matrix}\right.\)

=> x = 1/2 hoặc x=4

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

=>\(\left[{}\begin{matrix}x-1=0\\x+2=0\\x-3=0\end{matrix}\right.\)

=> \(\left[{}\begin{matrix}x=1\\x=-2\\x=3\end{matrix}\right.\)

Em ơi, với mấy bài có tích bằng 0 như này ta chỉ cần đặt từng trường hợp cho thừa số chứa biến x bằng 0; rồi giải phép tính là ra em nhé!

Mà cô có thắc mắc là đây là môn Toán, mình up lên môn Toán chứ sao lại môn Tiếng Anh bạn Kim nhỉ!

1: Ta có: \(\left(x+3\right)^2-\left(x+2\right)\left(x-2\right)=4x+17\)

\(\Leftrightarrow x^2+6x+9-x^2+4-4x=17\)

\(\Leftrightarrow x=2\)

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

\(\Leftrightarrow2x^2-2x+3x-3+2x-2x^2-3+3x=0\)

\(\Leftrightarrow6x=6\)

hay x=1

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

\(\Rightarrow\left[{}\begin{matrix}x-1=0\\2x+1=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=1\\x=-0,5\end{matrix}\right.\)

2/ x (2x-1) (3x+15) =0

\(\Rightarrow\left[{}\begin{matrix}x=0\\2x-1=0\\3x+15=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=0\\x=0,5\\x=-5\end{matrix}\right.\)

3/ (2x-6) (3x+4).x=0

\(\Rightarrow\left[{}\begin{matrix}2x-6=0\\3x+4=0\\x=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=3\\x=-\dfrac{4}{3}\\x=0\end{matrix}\right.\)

4/ (2x-10)(x²+1)=0

\(\Rightarrow\left[{}\begin{matrix}2x-10=0\\x^2+1=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=5\\x^2=-1\left(loại\right)\end{matrix}\right.\)

5/ (x²+3) (2x-1) =0

\(\Rightarrow\left[{}\begin{matrix}x^2+3=0\\2x-1=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x^2=-3\left(loại\right)\\x=0,5\end{matrix}\right.\)

6/ (3x-1) (2x² +1)=0

\(\Rightarrow\left[{}\begin{matrix}3x-1=0\\2x^2+1=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=-\dfrac{1}{3}\\x^2=-0,5\left(loại\right)\end{matrix}\right.\)

1: Ta có: \(\left(x-1\right)\left(2x+1\right)=0\)

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

2: Ta có: \(x\left(2x-1\right)\left(3x+15\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\2x-1=0\\3x+15=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{1}{2}\\x=-5\end{matrix}\right.\)

3: Ta có: \(\left(2x-6\right)\left(3x+4\right)x=0\)

\(\Leftrightarrow\left[{}\begin{matrix}2x-6=0\\3x+4=0\\x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-\dfrac{4}{3}\\x=0\end{matrix}\right.\)

4: Ta có: \(\left(2x-10\right)\left(x^2+1\right)=0\)

mà \(x^2+1>0\forall x\)

nên 2x-10=0

hay x=5

5: Ta có: \(\left(x^2+3\right)\left(2x-1\right)=0\)

mà \(x^2+3>0\forall x\)

nên 2x-1=0

hay \(x=\dfrac{1}{2}\)

6: Ta có: \(\left(3x-1\right)\left(2x^2+1\right)=0\)

mà \(2x^2+1>0\forall x\)

nên 3x-1=0

hay \(x=\dfrac{1}{3}\)

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

=>x=5 hoặc x=-3

2: =>(x-1)(5x-1)=0

=>x=1/5 hoặc x=1

5: =>(x-4)*x=0

=>x=0 hoặc x=4

10: =>(x+5)(x-3)=0

=>x=3 hoặc x=-5

9: =>(x-2)(x-4)=0

=>x=2 hoặc x=4

7: =>(x-6)(2x-1)=0

=>x=1/2 hoặc x=6

8: =>(2x-1)(3x-12)=0

=>x=4 hoặc x=1/2

1 

(3x-2)(4x+5)=0

⇔ 3x-2=0  -> x= 2/3      

 ⇔ 4x-5=0     x= 5/4

Vậy tập nghiệm S = { 2/3; 5/4}

2,    (4x+2)(\(X^2\)+3)=0

⇔ 4x+2=0         ->   x= -1/2    

     \(x^2\)+3=0         -> x= \(\sqrt{3}\); -\(\sqrt{3}\)

Vaayj tập nghiệm S= { -1/2; \(\sqrt{3}\);-\(\sqrt{3}\)}

3)

    (2x+7)(x-3)(5x-1)=0

⇔ 2x+7=0          ->   x= -7/2

     x-3   =0         ->     x =  3

    5x-1  =0         ->    x=  1/5

Vậy tập nghiệm S={ -7/2; 3; 1/5}

1) \(\Rightarrow10x-16-12x+15=12x-16+11\)

\(\Rightarrow14x=4\Rightarrow x=\dfrac{2}{7}\)

2) \(\Rightarrow4x^2+4x+1-4x^2+13x-3-15=0\)

\(\Rightarrow17x=17\Rightarrow x=1\)

3) \(\Rightarrow\left(3x-1\right)\left(2x-7+6x-5\right)=0\)

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

\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=\dfrac{1}{3}\end{matrix}\right.\)

2: Ta có: \(\left(2x+1\right)^2-\left(4x-1\right)\left(x-3\right)-15=0\)

\(\Leftrightarrow4x^2+4x+1-4x^2+12x+x-3-15=0\)

\(\Leftrightarrow17x=17\)

hay x=1

1.

 \(x^2-5x+6=0\\ \Rightarrow x^2-2x-3x+6=0\\ \Rightarrow\left(x^2-2x\right)-\left(3x-6\right)=0\\ \Rightarrow x\left(x-2\right)-3\left(x-2\right)=0\\ \Rightarrow\left(x-2\right)\left(x-3\right)=0\\ \Rightarrow\left[{}\begin{matrix}x-2=0\\x-3=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=2\\x=3\end{matrix}\right.\)

2.

\(\left(x+4\right)^2-\left(3x-1\right)^2=0\\ \Rightarrow\left(x+4-3x+1\right)\left(x+4+3x-1\right)=0\\ \Rightarrow\left(-2x+5\right)\left(4x+3\right)=0\\ \Rightarrow\left[{}\begin{matrix}-2x+5=0\\4x+3=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=\dfrac{5}{2}\\x=-\dfrac{3}{4}\end{matrix}\right.\)

3.

\(x^2-2x+24=0\\ \Rightarrow\left(x^2-2x+1\right)+23=0\\ \Rightarrow\left(x-1\right)^2+23=0\)

Vì (x-1)²≥0

23>0

\(\Rightarrow\left(x-1\right)^2+23>0\)

Vậy x vô nghiệm

4.

\(9x^2-4=0\\ \Rightarrow\left(3x-4\right)\left(3x+4\right)=0\\ \Rightarrow\left[{}\begin{matrix}3x-4=0\\3x+4=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=\dfrac{4}{3}\\x=-\dfrac{4}{3}\end{matrix}\right.\)

5.

\(x^2+2x-8=0\\ \Rightarrow\left(x^2+2x+1\right)-9=0\\ \Rightarrow\left(x+1\right)^2-3^2=0\\ \Rightarrow\left(x-2\right)\left(x+4\right)=0\\ \Rightarrow\left[{}\begin{matrix}x-2=0\\x+4=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=2\\x=-4\end{matrix}\right.\)