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

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

\(\Rightarrow\left[\begin{array}{nghiempt}\left(x-7\right)^{x+1}=0\\1-\left(x-7\right)^{10}=0\end{array}\right.\)\(\Rightarrow\left[\begin{array}{nghiempt}x-7=0\\\left(x-7\right)^{10}=1\end{array}\right.\)\(\Rightarrow\left[\begin{array}{nghiempt}x-7=0\\x-7=1\\x-7=-1\end{array}\right.\)\(\Rightarrow\left[\begin{array}{nghiempt}x=7\\x=8\\x=6\end{array}\right.\)

Vậy \(\left[\begin{array}{nghiempt}x=7\\x=8\\x=6\end{array}\right.\) thỏa mãn đề bài

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

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

\(\Rightarrow x-7=0\) hoặc \(1-\left(x-7\right)^{10}=0\)

+) \(x-7=0\Rightarrow x=7\)

+) \(1-\left(x-7\right)^{10}=0\)

\(\Rightarrow x-7=\pm1\)

+ \(x-7=1\Rightarrow x=8\)

+ \(x-7=-1\Rightarrow x=6\)

Vậy \(x\in\left\{7;8;6\right\}\)

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

\(\Rightarrow x-7=0\) hoặc \(x+1=x+11=0\) (vô lí vì \(1\ne11\) )

\(\Rightarrow x-7=0\Rightarrow x=7\)

My room is small, but it beautiful and my room has a table, a chair, a bed. Something, my room is dirty. Weekend, I always tidy my room. On the wall, I put some picture here. I love my room.

Like a paradise, my room is the only place where I feel free, warm and comfotable for relaxing after a tiring day at school. 
My room has simple design and everything looks neat and clear. It's a beautiful room because it is decorated by myself. I use bright color for the wall and blue ties to inspire an intimate feeling to the space. Besides, my room looks warm and airy with two huge windows on the two sides of the room. It's more lovely senery pictures and some lamps on the wall. I like the computer in my room most because it helps me a lot for my study. 
In my house I like my room most, I myself can do everything in it. I'm the owner of my own space so I always try to keep it clear and neat

Like a paradise, my room is the only place where I feel free, warm and comfotable for relaxing after a tiring day at school.
My room has simple design and everything looks neat and clear. It's a beautiful room because it is decorated by myself. I use bright color for the wall and blue ties to inspire an intimate feeling to the space. Besides, my room looks warm and airy with two huge windows on the two sides of the room. It's more lovely senery pictures and some lamps on the wall. I like the computer in my room most because it helps me a lot for my study.
In my house I like my room most, I myself can do everything in it. I'm the owner of my own space so I always try to keep it clear and neat.

Đề bài vẫn chưa đúng nhé, đúng ra phải là \(M=\frac{1}{ab+a+1}+\frac{1}{bc+b+1}+\frac{1}{abc+ac+c}\)

Ta có : \(M=\frac{1}{ab+a+1}+\frac{1}{bc+b+1}+\frac{1}{abc+ac+c}\)

\(=\frac{1}{ab+a+1}+\frac{a}{abc+ab+a}+\frac{ab}{a^2b^2c+a^2bc+abc}\)

\(=\frac{1}{ab+a+1}+\frac{a}{ab+a+1}+\frac{ab}{ab+a+1}=\frac{ab+a+1}{ab+a+1}=1\)

Vì a.b.c = 1

Ta có :

\(\frac{1}{ab+a+1}=\frac{c}{abc+ac+c}=\frac{c}{1+ac+c}\)

\(\frac{1}{bc+b+1}=\frac{ca}{bc.ca+abc+ca}=\frac{ca}{c+ca+1}\)

\(\frac{1}{abc+bc+b}=\frac{ac}{abc.ac+bc.ac+b.ac}=\frac{ac}{ac+c+1}\)

\(\Rightarrow M=\frac{c}{1+ac+c}+\frac{ca}{c+ca+1}+\frac{ac}{ac+c+1}\)

\(\Rightarrow M=\frac{c+2ac}{1+ac+c}\)

\(\Rightarrow M=\frac{bc+2}{b+1+bc}\)

\(\Rightarrow M=\frac{bc++1+abc}{b+1+bc}\)

-_-

Năm ngoái a lm ko ra thế này đâu

soyeon_Tiểubàng giải

c này mk tìm ra cách giải  r nhé

_giải sao vậy bạn?

\(xy-3x-y=4\Leftrightarrow x\left(y-3\right)-\left(y-3\right)=7\Leftrightarrow\left(x-1\right)\left(y-3\right)=7\)

Phân tích 7 = 1.7 = (-1).(-7) = ...........

Từ đó ghép cặp và tính.

Giải:

Ta có:

xy - 3x - y = 4

x.( y - 3 ) = 4 + y

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

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

( y - 3 ).( x - 1  ) = 7

Ta có bảng sau:

Vậy các cặp số ( x ; y ) là: ( 10 ; 2 );( 4 ; 8 );( 2; -6 );( -4 ; 0 )

xy-3x-y=4

=>xy-3x-y+3=7

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

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

Ta có bảng sau:

Vậy ...

|2x - 3| + x = 2

=> |2x - 3| = 2 - x

+ Với \(x< \frac{3}{2}\) thì |2x - 3| = 3 - 2x

Ta có: 3 - 2x = 2 - x

=> 3 - 2 = -x + 2x

=> x = 1, thỏa mãn \(x< \frac{3}{2}\)

+ Với \(x\ge\frac{3}{2}\) thì |2x - 3| = 2x - 3

Ta có: 2x - 3 = 2 - x

=> 2x + x = 2 + 3

=> 3x = 5

=> \(x=\frac{5}{3}\), thỏa mãn \(x\ge\frac{3}{2}\)

Vậy \(\left[\begin{array}{nghiempt}x=1\\x=\frac{5}{3}\end{array}\right.\)