a.x=9
b.x=5

Nhắc lại kiến thức  \(!a!=a,,,,\forall a\ge0\)

a) !2x-6!=2x-6 với mọi 2x-6>=0=> x>=3 

b) 3-x=!x-3!=!3-x! với mọi 3-x>=0=> x<=3

c)\(C=x^2-2x+3=x^2-x-x+1+2=x\left(x-1\right)-\left(x-1\right)+2=\left(x-1\right)^2+2\)

để C chia hết cho (x-1) => 2 phải chia hết cho (x-1)

x-1=U(2)={-2,-1,1,2}

x={-1,0,2,3}

Lồn mẹ mày

a) Có: \(\left|x-2\right|\ge0\)

\(\left|x-10\right|\ge0\)

\(\Rightarrow\left|x-2\right|+\left|x-10\right|+4\ge4\)

Xét \(\orbr{\begin{cases}x-2=0\Rightarrow x=2\Rightarrow A=0+8+4=12\\x-10=0\Rightarrow x=10\Rightarrow A=8+0+4=12\end{cases}}\)

Vậy \(Min_A=12\) tại \(x=2\) hoặc \(10\)

b) Có: \(\left|x-1\right|\ge0\)

\(\left|x-2\right|\ge0\)

\(\left|x-3\right|\ge0\)

\(\Rightarrow B\ge0\)

Xét: \(\hept{\begin{cases}x-1=0\Rightarrow x=1\Rightarrow B=0+1+2=3\\x-2=0\Rightarrow x=2\Rightarrow B=1+0+1=2\\x-3=0\Rightarrow x=3\Rightarrow B=2+1+0=3\end{cases}}\)

Vậy \(Min_B=2\) tại \(x=2\)

a)để -3/x-1 thuộc Z

=>-3 chia hết x-1

=>x-1\(\in\){1,-1,3,-3}

=>x\(\in\){2,0,4,-2}

b)để -4/2x-1 thuộc Z

=>4 chia hết 2x-1

=>2x-1\(\in\){1,-1,2,-2,4,-4}

=>x\(\in\){1;-3;3;-5;7;-9}

c)\(\frac{3x+7}{x-1}=\frac{3\left(x-1\right)+10}{x-1}=\frac{3\left(x-1\right)}{x-1}+\frac{10}{x-1}\in Z\)

=>10 chia hết x-1

=>x-1\(\in\)Ư(10)

bạn tự làm tiếp nhé

\(x\in Z\)\(\Rightarrow x+1\ne0\Rightarrow x\ne-1\)

Gọi d=(x-4,x+1)

\(\Rightarrow\hept{\begin{cases}x-4⋮d\\x+1⋮d\end{cases}}\)

\(\Rightarrow x+1-\left(x-4\right)⋮d\)\(\Rightarrow5⋮d\)

Giả sử d=5

=> \(x=5k+4\left(k\in Z\right)\)

mà \(\frac{x-4}{x+1}\)là phân số tối giản nên d=1

=>\(x\ne5k+4\)

`|x-2|=2x-3(x>=3/2)`

`<=>` \(\left[ \begin{array}{l}x-2=2x-3\\x-2=3-2x\end{array} \right.\) 

`<=>` \(\left[ \begin{array}{l}x=1(l)\\3x=5\end{array} \right.\) 

`<=>x=5/3(Tm(`

`2)A=-x^2+2x+9`

`=-(x^2-2x)+9`

`=-(x^2-2x+1)+1+9`

`=-(x-1)^2+10<=10`

Dấu "=" xảy ra khi `x=1.`

1,

* \(|x-2|=x-2< =>x\ge2\)

\(=>x-2=2x-3< =>x=1\left(ktm\right)\)

*\(\left|x-2\right|=2-x< =>x< 2\)

\(=>2-x=2x-3< =>x=\dfrac{5}{3}\left(tm\right)\)

vậy x=5/3

2, \(A=-x^2+2x+9=-\left(x^2-2x-9\right)=-\left(x^2-2x+1-10\right)\)

\(=-\left[\left(x-1\right)^2-10\right]=-\left(x-1\right)^2+10\le10\)

dấu"=" xảy ra<=>x=1

Bài 1: 

Ta có: \(\left|x-2\right|=2x-3\)

\(\Leftrightarrow\left[{}\begin{matrix}x-2=2x-3\left(x\ge2\right)\\2-x=2x-3\left(x< 2\right)\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x-2x=-3+2\\-x-2x=-3-2\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}-x=-1\\-3x=-5\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\left(lọai\right)\\x=\dfrac{5}{3}\left(nhận\right)\end{matrix}\right.\)

Vậy: \(S=\left\{\dfrac{5}{3}\right\}\)

a: \(A=\left(\dfrac{1}{x-1}+\dfrac{x}{\left(x-1\right)\left(x^2+x+1\right)}\cdot\dfrac{x^2+x+1}{x+1}\right)\cdot\dfrac{\left(x+1\right)^2}{2x+1}\)

\(=\left(\dfrac{1}{x-1}+\dfrac{x}{\left(x-1\right)\left(x+1\right)}\right)\cdot\dfrac{\left(x+1\right)^2}{2x+1}\)

\(=\dfrac{x+1+x}{\left(x-1\right)\left(x+1\right)}\cdot\dfrac{\left(x+1\right)^2}{2x+1}\)

\(=\dfrac{2x+1}{x-1}\cdot\dfrac{x+1}{2x+1}=\dfrac{x+1}{x-1}\)

b: Thay x=1/2 vào A, ta được:

\(A=\dfrac{\dfrac{1}{2}+1}{\dfrac{1}{2}-1}=\dfrac{3}{2}:\dfrac{-1}{2}=-3\)

c: Để A là số nguyên thì \(x-1+2⋮x-1\)

\(\Leftrightarrow x-1\in\left\{1;-1;2;-2\right\}\)

\(\Leftrightarrow x\in\left\{2;0;3\right\}\)

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