1,x=3 hoặc x=-2

2,x=12

3,không có x nào thỏa mãn

Bài 1 : 

Ta có : 

\(\left|2x-1\right|=5\)

\(\Leftrightarrow\)\(\orbr{\begin{cases}2x-1=5\\2x-1=-5\end{cases}\Leftrightarrow\orbr{\begin{cases}2x=6\\2x=-4\end{cases}}}\)

\(\Leftrightarrow\)\(\orbr{\begin{cases}x=\frac{6}{2}\\x=\frac{-4}{2}\end{cases}\Leftrightarrow\orbr{\begin{cases}x=3\\x=-2\end{cases}}}\)

Vậy \(x=-2\) hoặc \(x=3\)

Bài 2 : 

Đặt \(A=\frac{3x+4}{x-1}\) ta có : 

\(A=\frac{3x+4}{x-1}=\frac{3x-3+7}{x-1}=\frac{3x-3}{x-1}+\frac{7}{x-1}=\frac{3\left(x-1\right)}{x-1}+\frac{7}{x-1}=3+\frac{7}{x-1}\)

Để A là số nguyên thì \(\frac{7}{x-1}\) phải nguyên \(\Rightarrow\)\(7⋮\left(x-1\right)\)\(\Rightarrow\)\(\left(x-1\right)\inƯ\left(7\right)\)

Mà \(Ư\left(7\right)=\left\{1;-1;7;-7\right\}\)

Suy ra : 

Vậy \(x\in\left\{-6;0;2;8\right\}\) thì \(A\inℤ\)

Chúc bạn học tốt ~ 

a. Ta có: \(x^2-10x+26+y^2+2y=0\Leftrightarrow\left(x^2-10x+25\right)+\left(y^2+2y+1\right)=0\\ \)

\(\Leftrightarrow\left(x+5\right)^2+\left(y+1\right)^2=0\Rightarrow\hept{\begin{cases}x+5=0\\y+1=0\end{cases}\Leftrightarrow\hept{\begin{cases}x=-5\\y=-1\end{cases}}}\)

b. \(\left(2x+5\right)^2-\left(x-7\right)^2=0\Leftrightarrow\left(2x+5+x-7\right).\left(2x+5-x+7\right)=0\)

\(\Leftrightarrow\left(3x-2\right).\left(x+12\right)=0\Leftrightarrow\orbr{\begin{cases}3x-2=0\\x+12=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=\frac{2}{3}\\x=-12\end{cases}}}\)

c. \(25.\left(x-3\right)^2=49.\left(1-2x\right)^2\Leftrightarrow\left(5x-15\right)^2=\left(7-14x\right)^2\Leftrightarrow\left(5x-15\right)^2-\left(7-14x\right)^2=0\)

\(\Leftrightarrow\left(5x-15-7+14x\right).\left(5x-15+7-14x\right)=0\Leftrightarrow\left(19x-22\right).\left(-9x-8\right)=0\)

\(\Leftrightarrow\left(19x-22\right).\left(9x+8\right)=0\Leftrightarrow\orbr{\begin{cases}19x-22=0\\9x+8=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=\frac{22}{19}\\x=-\frac{8}{9}\end{cases}}}\)

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

\(\Leftrightarrow\left(4x-3\right).\left(8-2x\right)=0\Leftrightarrow\orbr{\begin{cases}4x-3=0\\8-2x=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=\frac{3}{4}\\x=4\end{cases}}}\)

e. \(x^2-2x+1=16\Leftrightarrow\left(x-1\right)^2-16=0\Leftrightarrow\left(x-1-4\right).\left(x-1+4\right)=0\)

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

Cảm ơn bn rất nhìu nha!!!^-^!!!

Bn ơi cho mik hỏi cái này đc ko ở câu a hai số cộng vs nhau bằng 0 thì một trong hai số đó là băng 0 à bn . Hi hi mik lại nghĩ là hai số nhân vs nhau bằng 0 thì 1 trong hai số đó ms bằng 0 chứ!!! Dù sao thì cx cảm ơn bn nhìu nà!!! Chúc bn học tốt nha!!!

Mk ko biết  kb nha 

ko bít

ko bít thì ko cần trả lời

1) Ta có: \(4x^2-1=\left(2x+1\right).\left(3x-5\right)\)

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

\(\Leftrightarrow\left(2x+1\right).\left[\left(2x-1\right)-\left(3x-5\right)\right]=0\)

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

\(\Leftrightarrow\left(2x+1\right).\left(4-x\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}2x+1=0\\4-x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=-1\\-x=-4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\frac{1}{2}\left(TM\right)\\x=4\left(TM\right)\end{matrix}\right.\)

Vậy \(x=-\frac{1}{2}\) hoặc \(x=4\)

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

\(\Leftrightarrow\left(x+1\right)^2-\left[2.\left(x-1\right)\right]^2=0\)

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

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

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

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

Vậy \(x=\frac{1}{3}\) hoặc \(x=3\)

3) Ta có: \(2x^3+5x^2-3x=0\)

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

\(\Leftrightarrow x.\left(2x^2-x+6x-3\right)=0\)

\(\Leftrightarrow x.\left[x.\left(2x-1\right)+3.\left(2x-1\right)\right]=0\)

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

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

Vậy \(x=0\) hoặc \(x=-3\) hoặc \(x=-\frac{1}{2}\)

4) Ta có: \(2x=3x-2\)

\(\Leftrightarrow2x-3x=-2\)

\(\Leftrightarrow-x=-2\)

\(\Leftrightarrow x=2\left(TM\right)\)

Vậy \(x=2\)

5) Ta có: \(x+15=3x-1\)

\(\Leftrightarrow x-3x=-1-15\)

\(\Leftrightarrow-2x=-16\)

\(\Leftrightarrow x=8\left(TM\right)\)

Vậy \(x=8\)

6) Ta có: \(2-x=0,5x-4\)

\(\Leftrightarrow-x-0,5x=-4-2\)

\(\Leftrightarrow-1,5x=-6\)

\(\Leftrightarrow x=4\left(TM\right)\)

Vậy \(x=4\)

1) 4x²-1=(2x+1)(3x-5)

<=> (2x-1)(2x+1)-(2x+1)(3x-5)=0

<=> (2x+1)(2x-1-3x+5)=0

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

<=>\([^{2x+1=0}_{4-x=0}< =>[^{2x=-1}_{x=4}< =>[^{x=\frac{-1}{2}}_{x=4}\)

2) (x+1)²= 4(x²-2x+1)

<=> x²+2x+1-4(x²-2x+1)=0

<=> x²+2x+1-4x²+8x-4=0

<=> -3x²+10x-3=0

<=> -3x²+x+9x-3=0

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

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

<=> \([^{3x-1=0}_{3-x=0}< =>[^{3x=1}_{x=3}< =>[^{x=\frac{1}{3}}_{x=3}\)

3) 2x³+5x²-3x=0

<=> 2x(x²+\(\frac{5}{2}x-\frac{3}{2})=0\)

<=> 2x\(\left[x^2+2.\frac{5}{4}x+\frac{25}{16}-\left(\frac{25}{16}+\frac{3}{2}\right)\right]=0\)

<=> 2x\(\left[\left(x+\frac{5}{4}\right)^2-\frac{49}{16}\right]=0\)

<=> 2x\(\left(x+\frac{5}{4}-\frac{7}{4}\right)\left(x+\frac{5}{4}+\frac{7}{4}\right)=0\)

<=> x\(\left(x-\frac{1}{2}\right)\left(x+3\right)=0\)

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

4) 2x=3x-2

<=> 2x-3x=-2

<=> -x=-2

<=> x=2

5) x+15=3x-1

<=> x-3x=1-15

<=> -2x=-14

<=> x=-14:-2

<=> x=7

6) 2-x=0,5x-4

<=> -x-0,5x=-4-2

<=> -1,5x=-6

<=> x= -6: -1,5

<=> x=4

học tốt nghen

1, \(4x^2-1=\left(2x+1\right)\left(3x-5\right)\)

\(\Leftrightarrow4x^2-1=6x^2-10x+3x-5\)

\(\Leftrightarrow4x^2-1=6x^2-7x-5\)

\(\Leftrightarrow6x^2-7x-5-4x^2+1=0\)

\(\Leftrightarrow2x^2-7x-4=0\)

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

\(\Leftrightarrow2x\left(x-4\right)-\left(x-4\right)=0\)

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

Vậy phương trình có tập nghiệm là \(S=\left\{4;\frac{1}{2}\right\}\)

2, \(\left(x+1\right)^2=4\left(x^2-2x+1\right)\)

\(\Leftrightarrow x^2+2x+1=4x^2-8x+4\\ \Leftrightarrow4x^2-8x+4-x^2-2x-1=0\\ \Leftrightarrow3x^2-10x+3=0\\ \Leftrightarrow\left(3x^2-x\right)-\left(9x-3\right)=0\\ \Leftrightarrow x\left(3x-1\right)-3\left(3x-1\right)=0\\ \Leftrightarrow\left(3x-1\right)\left(x-3\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}3x-1=0\\x-3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\frac{1}{3}\\x=3\end{matrix}\right.\)

Vậy phương trình có tập nghiệm là \(S=\left\{3;\frac{1}{3}\right\}\)

3,

\(2x^3+5x^2-3x=0\\ \Leftrightarrow x\left(2x^2+5x-3\right)=0\\ \Leftrightarrow x\left[\left(2x^2+x\right)-\left(6x+3\right)\right]=0\\ \Leftrightarrow x\left[x\left(2x+1\right)-3\left(2x+1\right)\right]=0\\ \Leftrightarrow x\left(2x+1\right)\left(x-3\right)=0\\ \left[{}\begin{matrix}x=0\\2x+1=0\\x-3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-\frac{1}{2}\\x=3\end{matrix}\right.\)

Vậy phương trình có tập nghiệm là \(S=\left\{0;-\frac{1}{2};3\right\}\)

câu a giống Võ Đoan Nhi

câu b: 

( x² + 2x -11 ) : ( x + 2)

=> x²  + 2x -11 : ( x + 2)

=> x(x+2) -11 : ( x + 2)

Vì x( x + 2) : ( x + 2) nên  -11 : ( x + 2)

=> x + 2 thuộc ước của -11

ta lập bảng..............

\(3x+4⋮x-3\)

\(\Leftrightarrow3\left(x-3\right)+10\)\(⋮x-3\)

-Mà: \(3\left(x-3\right)⋮x-3\Rightarrow10⋮x-3\)

\(\Leftrightarrow x-3\inƯ\left(10\right)\Leftrightarrow x-3\in\left\{\pm1;\pm2;\pm5;\pm10\right\}\)

-Lập bảng:.....