2x=3y=4z =k

suy ra x=k/2; y=k/3, z=k/4

mà xy + yz + zx = 6

suy ra \(\frac{k^2}{6}+\frac{k^2}{12}+\frac{k^2}{8}=6\Rightarrow k^2.\frac{3}{8}=6\Rightarrow k^2=16\Rightarrow k\in\left\{4;-4\right\}\)

Với k = 4 suy ra x =2; y=4/3; z=1

Với k =- 4 suy ra x =-2; y=-4/3; z=-1

Ta có :

\(2x=3y\Leftrightarrow\frac{x}{3}=\frac{y}{2}\)

                   \(\Leftrightarrow\frac{x}{6}=\frac{y}{4}\)

\(3y=4z\Leftrightarrow\frac{z}{3}=\frac{y}{4}\)

\(\Rightarrow\frac{x}{6}=\frac{y}{4}=\frac{z}{3}\)

Ta có :

\(\left(\frac{x}{6}\right)^2=\frac{x}{6}.\frac{x}{6}=\frac{x}{6}.\frac{y}{4}=\frac{y}{4}.\frac{z}{3}=\frac{z}{3}.\frac{y}{6}\)

\(\Leftrightarrow\)\(\left(\frac{x}{6}\right)^2\)\(=\frac{xy}{24}=\frac{yz}{12}=\frac{zx}{18}=\frac{xy+yz+zx}{24+12+18}=\frac{1}{9}\)\(\left(\text{T/c dãy tỉ số bằng nhau}\right)\)

\(\Rightarrow\frac{x}{6}=\frac{y}{4}=\frac{z}{3}\)\(=\pm\frac{1}{3}\)

\(\frac{1}{3}+2019x+\frac{2}{3}+2020x=4040x\)

\(\Rightarrow\frac{1}{3}+\frac{2}{3}+2019x+2020x=4040x\)

\(\Rightarrow1=4040x-2020x-2019x\)

\(\Rightarrow1=x\)

\(\Rightarrow x=1\)

Vậy x=1

Chúc bn học tốt

bạn viết bằng cả trái tim nhé sẽ hay hơn đấy

Là sao bạn?

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Bài làm của mình đó !

a)Để A có giá trị nguyên thì 3n+4 chia hết cho n-1

=>3(n-1)+7 chia hết cho n-1

=> n-1 thuộc Ư(7)={1;7;-1;-7}

Phần cuối bn tự làm nha

Còn câu b làm tương tự

a) Từ đề bài, ta có:

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

\(\Rightarrow\left(n-1\right)\inƯ\left(7\right)\)

\(\Rightarrow\left(n-1\right)\in\left\{\pm1;\pm7\right\}\)

\(\Rightarrow n\in\left\{2;0;-6;8\right\}\)

b) \(\frac{6n-3}{3n+1}=\frac{2\left(3n+1\right)+5}{3n+1}=2+\frac{5}{3n+1}\)

\(\Rightarrow\left(3n+1\right)\inƯ\left(5\right)\)

\(\Rightarrow\left(3n+1\right)\in\left\{\pm1;\pm5\right\}\)

\(\Rightarrow n\in\left\{\frac{-2}{3};0;-2;\frac{4}{3}\right\}\)

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ko hiểu

Rewrite the second sentences in the way that its meaning stays the same 

1What hobby do you best Mai?

=> What is your favorite hobby, Mai?

2The road was slippery so they couldn't drive fast 

=>Because the road was slippery, they couldn't drive fast .

3Her book is not the same as mine

=>Her book is different from mine.

4Collecting dolls is Lan interest

=>Lan is interested in/ fond of/ into  collecting dolls.

5We started to live here in 2012

=>We have lived here since 2012.

6People grow coffee in Brazil

=>Coffee was grown in Brazil.

7Her book is not the same as mine 

=>Her book is different from mine.

8You should road around the Old Quater at night 

=>It's a good idea to road around the Old Quater at night .

9I literatue best

=>My favourite subject is literature.

10American students have more vacations than Vietnamese students

=> Vietnamese students have fewer vacations than American students.

Ta có \(\hept{\begin{cases}xyz=1\\A=\frac{x}{xy+x+1}+\frac{y}{yz+y+1}+\frac{z}{xz+z+1}\end{cases}}\)

\(\Leftrightarrow A=\frac{x}{xy+x+1}+\frac{yx}{xyz+xy+x}+\frac{xyz}{x^2yz+xyz+xy}\)

\(\Leftrightarrow A=\frac{x}{xy+x+1}+\frac{yx}{x+xy+1}+\frac{1}{x+1+xy}\)

\(\Leftrightarrow A=\frac{x+xy+1}{xy+x+1}=1\)

Vậy A = 1

~~~ Học tốt

Takigawa Miraii 

Cách khác

Ta có \(\hept{\begin{cases}xyz=1\\A=\frac{x}{xy+x+1}+\frac{y}{yz+y+1}+\frac{z}{xz+z+1}\end{cases}}\)

<=> \(A=\frac{xyz}{xy^2z+xyz+yz}+\frac{y}{yz+y+1}+\frac{zy}{xyz+zy+y}\)

<=> \(A=\frac{1}{y+1+yz}+\frac{y}{yz+y+1}+\frac{zy}{1+zy+y}\)

<=> \(A=\frac{1+y+zy}{y+1+yz}=1\)

Vậy A = 1

Còn 4 cách nx