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25 tháng 10 2021

\(1,4x\left(x-5\right)-\left(x-1\right)\left(4x-3\right)=5\)

\(4x^2-20x-4x^2+3x-4x+3=5\)

\(-21x+3=5\)

\(21x=-8\)

\(x=-\frac{8}{21}\)

25 tháng 10 2021

\(2,8x^3-50x=0\)

\(x\left(8x^2-50\right)=0\)

\(\Rightarrow\hept{\begin{cases}x=0\\8x^2-50=0\Rightarrow x=\pm2\end{cases}}\)

Vậy ....

\(3,\left(2x-1\right)^2-25=0\)

\(\left(2x-1\right)^2=\pm5^2\)

\(\Rightarrow\hept{\begin{cases}2x-1=5\\2x-1=\left(-5\right)\end{cases}}\Rightarrow\hept{\begin{cases}x=3\\x=\left(-2\right)\end{cases}}\)

Vậy ... 

1: Ta có: \(\left(x+3\right)\left(x^2-3x+9\right)-\left(x^3+54\right)\)

\(=x^3+27-x^3-54\)

=-27

2: Ta có: \(\left(2x+y\right)\left(4x^2-2xy+y^2\right)-\left(2x-y\right)\left(4x^2+2xy+y^2\right)\)

\(=8x^3+y^3-8x^3+y^3\)

\(=2y^3\)

18 tháng 9 2021

\(1,=x^3+270-x^3-54=-27\\ 2,=8x^3+y^3-8x^3+y^3=2y^3\\ 3,=x^3-3x^2+3x-1-x^3-8+3x^2-48=3x-57\\ 4,=x^3-x-x^3-1=-x-1\\ 5,=8x^3-5\left(8x^3+1\right)=-32x^3-5\\ 6,=27+x^3-27=x^3\\ 7,làm.ở.câu.3\\ 8,=x^3-6x^2+12x-8+6x^2-12x+6-x^3-1+3x\\ =3x-3\)

AH
Akai Haruma
Giáo viên
2 tháng 10 2021

a. 

$x^4-6x^2+9=0$

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

$\Leftrightarrow x^2-3=0$

$\Leftrightarrow x^2=3$

$\Leftrightarrow x=\pm \sqrt{3}$

b.

$8x^3+12x^2+6x-63=0$

$\Leftrightarrow (8x^2+12x^2+6x+1)-64=0$

$\Leftrightarrow (2x+1)^3=64=4^3$

$\Leftrightarrow 2x+1=4$

$\Leftrightarrow x=\frac{3}{2}$

c. $(3-2x)^2-25=0$

$\Leftrightarrow (3-2x)^2-5^2=0$

$\Leftrightarrow (3-2x-5)(3-2x+5)=0$

$\Leftrightarrow (-2-2x)(8-2x)=0$

$\Leftrightarrow -2-2x=0$ hoặc $8-2x=0$

$\Leftrightarrow x=-1$ hoặc $x=4$

 

AH
Akai Haruma
Giáo viên
2 tháng 10 2021

d.

$6(x+1)^2-2(x+1)^3+2(x-1)(x^2+x+1)=1$

$\Leftrightarrow (x+1)^2[6-2(x+1)]+2(x^3-1)=1$

$\Leftrightarrow (x+1)^2(4-2x)+2x^3-3=0$

$\Leftrightarrow 6x+1=0$

$\Leftrightarrow x=\frac{-1}{6}$

e. $(x-2)^2-(x-2)(x+2)=0$

$\Leftrightarrow (x-2)[(x-2)-(x+2)]=0$

$\Leftrightarrow (x-2)(-4)=0$

$\Leftrightarrow x-2=0$

$\Leftrightarrow x=2$

f. $x^2-4x+4=25$

$\Leftrightarrow (x-2)^2=5^2=(-5)^2$

$\Leftrightarrow x-2=5$ hoặc $x-2=-5$

$\Leftrightarrow x=7$ hoặc $x=-3$

 

 

 

10 tháng 10 2021

a) (2x−1)2−25=0

(2x−1)2=0+25=25

(2x−1)2=52=(−5)2

⇒[2x−1=52x−1=−5⇒[2x=62x=−4⇒[x=3x=−2

b) 8x3−50x=0

10 tháng 10 2021

câu b thiếu bn ơi

10 tháng 10 2021

a: Ta có: \(\left(2x-1\right)^2-25=0\)

\(\Leftrightarrow\left(2x-6\right)\left(2x+4\right)=0\)

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

 

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

14 tháng 7 2023

`@` `\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}.`

29 tháng 10 2021

a: \(\Leftrightarrow\left(x-5\right)\left(x+1\right)\left(x-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=5\\x=-1\\x=1\end{matrix}\right.\)

d: \(\Leftrightarrow\left(x+3\right)\left(x^2-4x+5\right)=0\)

\(\Leftrightarrow x+3=0\)

hay x=-3

12 tháng 10 2023

a: \(x^2+4x+4=x^2+2\cdot x\cdot2+2^2=\left(x+2\right)^2\)

b: \(4x^2-4x+1=\left(2x\right)^2-2\cdot2x\cdot1+1^2=\left(2x-1\right)^2\)

c: \(2x-1-x^2\)

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

d: \(x^2+x+\dfrac{1}{4}=x^2+2\cdot x\cdot\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2=\left(x+\dfrac{1}{2}\right)^2\)

e: \(9-x^2=3^2-x^2=\left(3-x\right)\left(3+x\right)\)

g: \(\left(x+5\right)^2-4x^2=\left(x+5+2x\right)\left(x+5-2x\right)\)

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

h: \(\left(x+1\right)^2-\left(2x-1\right)^2\)

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

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

i: \(=x^2y^2-4xy+4-3\)

\(=\left(xy-2\right)^2-3=\left(xy-2-\sqrt{3}\right)\left(xy-2+\sqrt{3}\right)\)

k: \(=y^2-\left(x-1\right)^2\)

\(=\left(y-x+1\right)\left(y+x-1\right)\)

l: \(=x^3+3\cdot x^2\cdot2+3\cdot x\cdot2^2+2^3=\left(x+2\right)^3\)

m: \(=\left(2x\right)^3-3\cdot\left(2x\right)^2\cdot y+3\cdot2x\cdot y^2-y^3=\left(2x-y\right)^3\)

23 tháng 10 2021

e: ta có: \(4x^2+4x-6=2\)

\(\Leftrightarrow4x^2+4x-8=0\)

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

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

f: Ta có: \(2x^2+7x+3=0\)

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

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