\(\left(x-7\right)^x+1-\left(x-7\right)^x+11=0\)\(0\)

<=>\(\left(x-7\right)^x-\left(x-7\right)^x+12=0\)

<=>         \(12=0\)=> \(v\text{ô}\)\(l\text{ý}\)

Ko có giá trị của x

Ta có : \(\left(x-7\right)^{x+1}-\left(x-7\right)^{x+11}=0\)

=> (x - 7)^{x + 1}.[1 - (x - 7)¹⁰] = 0

=> \(\orbr{\begin{cases}\left(x-7\right)^{x+1}=0\\1-\left(x-7\right)^{10}=0\end{cases}}\Rightarrow\orbr{\begin{cases}\left(x-7\right)^{x+1}=0^{x+1}\\\left(x-7\right)^{10}=1^{10}\end{cases}\Rightarrow\orbr{\begin{cases}x-7=0\\x-7=\pm1\end{cases}}}\)

Nếu x - 7 = 0 => x = 7

Nếu x - 7 = 1 => x = 8

Nếu x - 7 = - 1 => x = 6

Vậy \(x\in\left\{6;7;8\right\}\)

\(a,2x\left(x-1\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}2x=0\\x-1=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x\in\forall Z\\x=1\end{cases}}}\)

\(b,x\left(2x-4\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x=0\\2x-4=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=0\\x=2\end{cases}}}\)

\(c;\left(x+1\right)+\left(x+3\right)+...............+\left(x+99\right)=0\)

\(\Rightarrow\left(x+x+...........+x\right)+\left(1+3+............+99\right)=0\)

\(\Rightarrow50x+2500=0\)

\(\Rightarrow50x=-2500\)

\(\Rightarrow x=-50\)

2/

\(a;\left(x-3\right)\left(2y+1\right)=7\)

\(\Rightarrow\left(x-3\right);\left(2y+1\right)\inƯ\left(7\right)=\left\{\pm1;\pm7\right\}\)

Xét bảng

Vậy...............................

\(b;xy+3x-2y=11\)

\(\Rightarrow x\left(y+3\right)-2y-6=11-6\)

\(\Rightarrow x\left(y+3\right)-2\left(y+3\right)=5\)

\(\Rightarrow\left(x-2\right)\left(y+3\right)=5\)

\(\Rightarrow\left(x-2\right);\left(y+3\right)\inƯ\left(5\right)=\left\{\pm1;\pm5\right\}\)

Xét bảng'

Vậy................................

\(\left(x-7\right)^{x+1}-\left(x-7\right)^{x+11}=0\)

\(\)\(\Rightarrow\left(x-7\right)^{x+1}.\left[1-\left(x-7\right)^{10}\right]=0\)

\(\Rightarrow\left[\begin{matrix}\left(x-7\right)^{x+1}=0\\1-\left(x-7\right)^{10}=0\end{matrix}\right.\)

\(\Rightarrow\left[\begin{matrix}x-7=0\\\left(x-7\right)^{10}=1\end{matrix}\right.\)

\(\Rightarrow\left[\begin{matrix}x-7=0\\\left[\begin{matrix}x-7=1\\x-7=-1\end{matrix}\right.\end{matrix}\right.\)

\(\Rightarrow\left[\begin{matrix}x=7\\\left[\begin{matrix}x=8\\x=6\end{matrix}\right.\end{matrix}\right.\)

Vậy....

                                                             Bài giải

\(\left(x-7\right)^{y+1}-\left(x-7\right)^{y+11}=0\)

\(\left(x-7\right)^{y+1}\left[1-\left(x-7\right)^{y+10}\right]=0\)

\(\Rightarrow\orbr{\begin{cases}\left(x-7\right)^{y+1}=0\\1-\left(x-7\right)^{y+10}=0\end{cases}}\)    \(\Rightarrow\orbr{\begin{cases}x-7=0\\\left(x-7\right)^{y+10}=1\end{cases}}\)\(\Rightarrow\orbr{\begin{cases}x=7\\x-7=1\text{ hoặc }y+10=0\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=7\\x=8\text{ hoặc }y=-10\end{cases}}\)

\(\Rightarrow\text{ }\left(x\text{ ; }y\right)\in\left(7\text{ ; }-10\right)\text{ ; }\left(8\text{ ; }-10\right)\)

Mình tưởng y bằng bao nhiêu cx đc vì phần cơ số bằng 0 hoặc 1 r còn gì.

Mk ko viết lại đề bài nhé

<=> -2-2-2-...-2=-100

<=>(-2)(\({\\{x-1} \over 4}\)+1)=-100

<=>\({\\{x-1} \over 4}\)+1=50

<=>\({\\{x-1} \over 4}\)=49

<=>x-1=196

<=>x=197

Nhớ k nha

x = 197

\(\Leftrightarrow\left(x-7\right)^{x-11}\left[\left(x-7\right)^{12}-1\right]=0\\ \Leftrightarrow\left[{}\begin{matrix}\left(x-7\right)^{x-11}=0\\\left(x-7\right)^{12}=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x-7=0\\x-7=1\\x-7=-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=7\\x=8\\x=6\end{matrix}\right.\)

\(\Leftrightarrow\left(x-7\right)^{x+1}\left[\left(x-7\right)-\left(x-7\right)^{12}\right]=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-7=0\\x-7=1\\x-7=-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=7\\x=8\\x=6\end{matrix}\right.\)

Câu 1:

(x-3)(y-1) = 7

Ư(7) = {-7; -1; 1; 7}

Lập bảng ta có:

Theo bảng trên ta có:

(x;y) = (-4; 0); (2; -6); (4; 8); (10; 2)

Vậy (x;y) = (-4; 0); (2; -6); (4; 8); (10; 2)

Câu 2:

xy + 3x - 7y = 21

(xy + 3x) - 7y = 21

x(y + 3) - (7y + 21) = 0

x(y+3) - 7(y+3) =0

(x-7)(y+3) = 0

x = 7, y ∈ Z

hoặc y = - 3 và x ∈ Z